LightOJ 1064 dp

/********************

LightOJ 1064

Author:Cdegree

********************/
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <algorithm>
#include <iostream>
#include <string>
#include <set>
#define X first
#define Y second
#define sqr(x) (x)*(x)
#pragma comment(linker,"/STACK:102400000,102400000")
using namespace std;
const double PI = acos(-1.0);
map<int, int>::iterator it;
typedef long long LL ;
template<typename T> void checkmin(T &x, T y) {x = min(x, y);}
template<typename T> void checkmax(T &x, T y) {x = max(x, y);}

#define DIGIT    4
#define DEPTH    10000
#define MAX     50
typedef int bignum_t[MAX+1];

int read(bignum_t a, istream& is = cin) {
    char buf[MAX*DIGIT+1], ch;
    int i, j;
    memset((void*)a, 0, sizeof(bignum_t));
    if(!(is >> buf))    return 0;
    for(a[0] = strlen(buf), i = a[0] / 2 - 1; i >= 0; i--)
        ch = buf[i], buf[i] = buf[a[0] - 1 - i], buf[a[0] - 1 - i] = ch;
    for(a[0] = (a[0] + DIGIT - 1) / DIGIT, j = strlen(buf); j < a[0]*DIGIT; buf[j++] = '0');
    for(i = 1; i <= a[0]; i++)
        for(a[i] = 0, j = 0; j < DIGIT; j++)
            a[i] = a[i] * 10 + buf[i*DIGIT-1-j] - '0';
    for(; !a[a[0]] && a[0] > 1; a[0]--);
    return 1;
}

void write(const bignum_t a, ostream& os = cout) {
    int i, j;
    for(os << a[i=a[0]], i--; i; i--)
        for(j = DEPTH / 10; j; j /= 10)
            os << a[i] / j % 10;
}

int comp(const bignum_t a, const bignum_t b) {
    int i;
    if(a[0] != b[0])
        return a[0] - b[0];
    for(i = a[0]; i; i--)
        if(a[i] != b[i])
            return a[i] - b[i];
    return 0;
}

int comp(const bignum_t a, const int b) {
    int c[12] = {1};
    for(c[1] = b; c[c[0]] >= DEPTH; c[c[0] + 1] = c[c[0]] / DEPTH, c[c[0]] %= DEPTH, c[0]++);
    return comp(a, c);
}

int comp(const bignum_t a, const int c, const int d, const bignum_t b) {
    int i, t = 0, O = -DEPTH * 2;
    if(b[0] - a[0] < d && c)
        return 1;
    for(i = b[0]; i > d; i--) {
        t = t * DEPTH + a[i-d] * c - b[i];
        if(t > 0) return 1;
        if(t < O) return 0;
    }
    for(i = d; i; i--) {
        t = t * DEPTH - b[i];
        if(t > 0) return 1;
        if(t < O) return 0;
    }
    return t > 0;
}

void add(bignum_t a, const bignum_t b) {
    int i;
    for(i = 1; i <= b[0]; i++)
        if((a[i] += b[i]) >= DEPTH)
            a[i] -= DEPTH, a[i+1]++;
    if(b[0] >= a[0])
        a[0] = b[0];
    else
        for(; a[i] >= DEPTH && i < a[0]; a[i] -= DEPTH, i++, a[i]++);
    a[0] += (a[a[0] + 1] > 0);
}

void add(bignum_t a, const int b) {
    int i = 1;
    for(a[1] += b; a[i] >= DEPTH && i < a[0]; a[i+1] += a[i] / DEPTH, a[i] %= DEPTH, i++);
    for(; a[a[0]] >= DEPTH; a[a[0] + 1] = a[a[0]] / DEPTH, a[a[0]] %= DEPTH, a[0]++);
}

void sub(bignum_t a, const bignum_t b) {
    int i;
    for(i = 1; i <= b[0]; i++)
        if((a[i] -= b[i]) < 0)
            a[i+1]--, a[i] += DEPTH;
    for(; a[i] < 0; a[i] += DEPTH, i++, a[i]--);
    for(; !a[a[0]] && a[0] > 1; a[0]--);
}

void sub(bignum_t a, const int b) {
    int i = 1;
    for(a[1] -= b; a[i] < 0; a[i+1] += (a[i] - DEPTH + 1) / DEPTH, a[i] -= (a[i] - DEPTH + 1) / DEPTH * DEPTH, i++);
    for(; !a[a[0]] && a[0] > 1; a[0]--);
}

void sub(bignum_t a, const bignum_t b, const int c, const int d) {
    int i, O = b[0] + d;
    for(i = 1 + d; i <= O; i++)
        if((a[i] -= b[i-d] * c) < 0)
            a[i+1] += (a[i] - DEPTH + 1) / DEPTH, a[i] -= (a[i] - DEPTH + 1) / DEPTH * DEPTH;
    for(; a[i] < 0; a[i+1] += (a[i] - DEPTH + 1) / DEPTH, a[i] -= (a[i] - DEPTH + 1) / DEPTH * DEPTH, i++);
    for(; !a[a[0]] && a[0] > 1; a[0]--);
}

void mul(bignum_t c, const bignum_t a, const bignum_t b) {
    int i, j;
    memset((void*)c, 0, sizeof(bignum_t));
    for(c[0] = a[0] + b[0] - 1, i = 1; i <= a[0]; i++)
        for(j = 1; j <= b[0]; j++)
            if((c[i+j-1] += a[i] * b[j]) >= DEPTH)
                c[i+j] += c[i+j-1] / DEPTH, c[i+j-1] %= DEPTH;
    for(c[0] += (c[c[0] + 1] > 0); !c[c[0]] && c[0] > 1; c[0]--);
}

void mul(bignum_t a, const int b) {
    int i;
    for(a[1] *= b, i = 2; i <= a[0]; i++) {
        a[i] *= b;
        if(a[i-1] >= DEPTH)
            a[i] += a[i-1] / DEPTH, a[i-1] %= DEPTH;
    }
    for(; a[a[0]] >= DEPTH; a[a[0] + 1] = a[a[0]] / DEPTH, a[a[0]] %= DEPTH, a[0]++);
    for(; !a[a[0]] && a[0] > 1; a[0]--);
}

void mul(bignum_t b, const bignum_t a, const int c, const int d) {
    int i;
    memset((void*)b, 0, sizeof(bignum_t));
    for(b[0] = a[0] + d, i = d + 1; i <= b[0]; i++)
        if((b[i] += a[i-d] * c) >= DEPTH)
            b[i+1] += b[i] / DEPTH, b[i] %= DEPTH;
    for(; b[b[0] + 1]; b[0]++, b[b[0] + 1] = b[b[0]] / DEPTH, b[b[0]] %= DEPTH);
    for(; !b[b[0]] && b[0] > 1; b[0]--);
}

void div(bignum_t c, bignum_t a, const bignum_t b) {
    int h, l, m, i;
    memset((void*)c, 0, sizeof(bignum_t));
    c[0] = (b[0] < a[0] + 1) ? (a[0] - b[0] + 2) : 1;
    for(i = c[0]; i; sub(a, b, c[i] = m, i - 1), i--)
        for(h = DEPTH - 1, l = 0, m = (h + l + 1) >> 1; h > l; m = (h + l + 1) >> 1)
            if(comp(b, m, i - 1, a)) h = m - 1;
            else l = m;
    for(; !c[c[0]] && c[0] > 1; c[0]--);
    c[0] = c[0] > 1 ? c[0] : 1;
}

void div(bignum_t a, const int b, int& c) {
    int i;
    for(c = 0, i = a[0]; i; c = c*DEPTH + a[i], a[i] = c / b, c %= b, i--);
    for(; !a[a[0]] && a[0] > 1; a[0]--);
}

void sqrt(bignum_t b, bignum_t a) {
    int h, l, m, i;
    memset((void*)b, 0, sizeof(bignum_t));
    for(i = b[0] = (a[0] + 1) >> 1; i; sub(a, b, m, i - 1), b[i] += m, i--)
        for(h = DEPTH - 1, l = 0, b[i] = m = (h + l + 1) >> 1; h > l; b[i] = m = (h + l + 1) >> 1)
            if(comp(b, m, i - 1, a)) h = m - 1;
            else l = m;
    for(; !b[b[0]] && b[0] > 1; b[0]--);
    for(i = 1; i <= b[0]; b[i++] >>= 1);
}

int length(const bignum_t a) {
    int t, ret;
    for(ret = (a[0] - 1) * DIGIT, t = a[a[0]]; t; t /= 10, ret++);
    return ret > 0 ? ret : 1;
}

int digit(const bignum_t a, const int b) {
    int i, ret;
    for(ret = a[(b-1)/DIGIT+1], i = (b - 1) % DIGIT; i; ret /= 10, i--);
    return ret % 10;
}

int zeronum(const bignum_t a) {
    int ret, t;
    for(ret = 0; !a[ret+1]; ret++);
    for(t = a[ret+1], ret *= DIGIT; !(t % 10); t /= 10, ret++);
    return ret;
}

void comp(int* a, const int l, const int h, const int d) {
    int i, j, t;
    for(i = l; i <= h; i++)
        for(t = i, j = 2; t > 1; j++)
            while(!(t % j))
                a[j] += d, t /= j;
}

void convert(int* a, const int h, bignum_t b) {
    int i, j, t = 1;
    memset(b, 0, sizeof(bignum_t));
    for(b[0] = b[1] = 1, i = 2; i <= h; i++)
        if(a[i])
            for(j = a[i]; j; t *= i, j--)
                if(t * i > DEPTH)
                    mul(b, t), t = 1;
    mul(b, t);
}

void combination(bignum_t a, int m, int n) {
    int* t = new int[m+1];
    memset((void*)t, 0, sizeof(int)*(m + 1));
    comp(t, n + 1, m, 1);
    comp(t, 2, m - n, -1);
    convert(t, m, a);
    delete []t;
}

void permutation(bignum_t a, int m, int n) {
    int i, t = 1;
    memset(a, 0, sizeof(bignum_t));
    a[0] = a[1] = 1;
    for(i = m - n + 1; i <= m; t *= i++)
        if(t * i > DEPTH)
            mul(a, t), t = 1;
    mul(a, t);
}

#define SGN(x) ((x)>0?1:((x)<0?-1:0))
#define ABS(x) ((x)>0?(x):-(x))

int read(bignum_t a, int &sgn, istream& is = cin) {
    char str[MAX*DIGIT+2], ch, *buf;
    int i, j;
    memset((void*)a, 0, sizeof(bignum_t));
    if(!(is >> str)) return 0;
    buf = str, sgn = 1;
    if(*buf == '-') sgn = -1, buf++;
    for(a[0] = strlen(buf), i = a[0] / 2 - 1; i >= 0; i--)
        ch = buf[i], buf[i] = buf[a[0] - 1 - i], buf[a[0] - 1 - i] = ch;
    for(a[0] = (a[0] + DIGIT - 1) / DIGIT, j = strlen(buf); j < a[0]*DIGIT; buf[j++] = '0');
    for(i = 1; i <= a[0]; i++)
        for(a[i] = 0, j = 0; j < DIGIT; j++)
            a[i] = a[i] * 10 + buf[i*DIGIT-1-j] - '0';
    for(; !a[a[0]] && a[0] > 1; a[0]--);
    if(a[0] == 1 && !a[1]) sgn = 0;
    return 1;
}

struct bignum {
    bignum_t num;
    int sgn;
public:
    inline bignum() {memset(num, 0, sizeof(bignum_t)); num[0] = 1; sgn = 0;}
    inline int operator!() {return num[0] == 1 && !num[1];}
    inline bignum& operator=(const bignum& a) {memcpy(num, a.num, sizeof(bignum_t)); sgn = a.sgn; return *this;}
    inline bignum& operator=(const int a) {memset(num, 0, sizeof(bignum_t)); num[0] = 1; sgn = SGN(a); add(num, sgn * a); return *this;};
    inline bignum& operator+=(const bignum& a) {
        if(sgn == a.sgn)add(num, a.num); else if(sgn && a.sgn) {
            int ret = comp(num, a.num); if(ret > 0)sub(num, a.num); else if(ret < 0) {
                bignum_t t;
                memcpy(t, num, sizeof(bignum_t)); memcpy(num, a.num, sizeof(bignum_t)); sub(num, t); sgn = a.sgn;
            }
            else memset(num, 0, sizeof(bignum_t)), num[0] = 1, sgn = 0;
        }
        else if(!sgn)memcpy(num, a.num, sizeof(bignum_t)), sgn = a.sgn; return *this;
    }
    inline bignum& operator+=(const int a) {
        if(sgn * a > 0)add(num, ABS(a)); else if(sgn && a) {
            int ret = comp(num, ABS(a)); if(ret > 0)sub(num, ABS(a)); else if(ret < 0) {
                bignum_t t;
                memcpy(t, num, sizeof(bignum_t)); memset(num, 0, sizeof(bignum_t)); num[0] = 1; add(num, ABS(a)); sgn = -sgn; sub(num, t);
            }
            else memset(num, 0, sizeof(bignum_t)), num[0] = 1, sgn = 0;
        }
        else if(!sgn)sgn = SGN(a), add(num, ABS(a)); return *this;
    }
    inline bignum operator+(const bignum& a) {bignum ret; memcpy(ret.num, num, sizeof(bignum_t)); ret.sgn = sgn; ret += a; return ret;}
    inline bignum operator+(const int a) {bignum ret; memcpy(ret.num, num, sizeof(bignum_t)); ret.sgn = sgn; ret += a; return ret;}
    inline bignum& operator-=(const bignum& a) {
        if(sgn * a.sgn < 0)add(num, a.num); else if(sgn && a.sgn) {
            int ret = comp(num, a.num); if(ret > 0)sub(num, a.num); else if(ret < 0) {
                bignum_t t;
                memcpy(t, num, sizeof(bignum_t)); memcpy(num, a.num, sizeof(bignum_t)); sub(num, t); sgn = -sgn;
            }
            else memset(num, 0, sizeof(bignum_t)), num[0] = 1, sgn = 0;
        }
        else if(!sgn)add(num, a.num), sgn = -a.sgn; return *this;
    }
    inline bignum& operator-=(const int a) {
        if(sgn * a < 0)add(num, ABS(a)); else if(sgn && a) {
            int ret = comp(num, ABS(a)); if(ret > 0)sub(num, ABS(a)); else if(ret < 0) {
                bignum_t t;
                memcpy(t, num, sizeof(bignum_t)); memset(num, 0, sizeof(bignum_t)); num[0] = 1; add(num, ABS(a)); sub(num, t); sgn = -sgn;
            }
            else memset(num, 0, sizeof(bignum_t)), num[0] = 1, sgn = 0;
        }
        else if(!sgn)sgn = -SGN(a), add(num, ABS(a)); return *this;
    }
    inline bignum operator-(const bignum& a) {bignum ret; memcpy(ret.num, num, sizeof(bignum_t)); ret.sgn = sgn; ret -= a; return ret;}
    inline bignum operator-(const int a) {bignum ret; memcpy(ret.num, num, sizeof(bignum_t)); ret.sgn = sgn; ret -= a; return ret;}
    inline bignum& operator*=(const bignum& a) {bignum_t t; mul(t, num, a.num); memcpy(num, t, sizeof(bignum_t)); sgn *= a.sgn; return *this;}
    inline bignum& operator*=(const int a) {mul(num, ABS(a)); sgn *= SGN(a); return *this;}
    inline bignum operator*(const bignum& a) {bignum ret; mul(ret.num, num, a.num); ret.sgn = sgn * a.sgn; return ret;}
    inline bignum operator*(const int a) {bignum ret; memcpy(ret.num, num, sizeof(bignum_t)); mul(ret.num, ABS(a)); ret.sgn = sgn * SGN(a); return ret;}
    inline bignum& operator/=(const bignum& a) {bignum_t t; div(t, num, a.num); memcpy(num, t, sizeof(bignum_t)); sgn = (num[0] == 1 && !num[1]) ? 0 : sgn * a.sgn; return *this;}
    inline bignum& operator/=(const int a) {int t; div(num, ABS(a), t); sgn = (num[0] == 1 && !num[1]) ? 0 : sgn * SGN(a); return *this;}
    inline bignum operator/(const bignum& a) {bignum ret; bignum_t t; memcpy(t, num, sizeof(bignum_t)); div(ret.num, t, a.num); ret.sgn = (ret.num[0] == 1 && !ret.num[1]) ? 0 : sgn * a.sgn; return ret;}
    inline bignum operator/(const int a) {bignum ret; int t; memcpy(ret.num, num, sizeof(bignum_t)); div(ret.num, ABS(a), t); ret.sgn = (ret.num[0] == 1 && !ret.num[1]) ? 0 : sgn * SGN(a); return ret;}
    inline bignum& operator%=(const bignum& a) {bignum_t t; div(t, num, a.num); if(num[0] == 1 && !num[1])sgn = 0; return *this;}
    inline int operator%=(const int a) {int t; div(num, ABS(a), t); memset(num, 0, sizeof(bignum_t)); num[0] = 1; add(num, t); return t;}
    inline bignum operator%(const bignum& a) {bignum ret; bignum_t t; memcpy(ret.num, num, sizeof(bignum_t)); div(t, ret.num, a.num); ret.sgn = (ret.num[0] == 1 && !ret.num[1]) ? 0 : sgn; return ret;}
    inline int operator%(const int a) {bignum ret; int t; memcpy(ret.num, num, sizeof(bignum_t)); div(ret.num, ABS(a), t); memset(ret.num, 0, sizeof(bignum_t)); ret.num[0] = 1; add(ret.num, t); return t;}
    inline bignum& operator++() {*this += 1; return *this;}
    inline bignum& operator--() {*this -= 1; return *this;};
    inline int operator>(const bignum& a) {return sgn > 0 ? (a.sgn > 0 ? comp(num, a.num) > 0 : 1) : (sgn < 0 ? (a.sgn < 0 ? comp(num, a.num) < 0 : 0) : a.sgn < 0);}
    inline int operator>(const int a) {return sgn > 0 ? (a > 0 ? comp(num, a) > 0 : 1) : (sgn < 0 ? (a < 0 ? comp(num, -a) < 0 : 0) : a < 0);}
    inline int operator>=(const bignum& a) {return sgn > 0 ? (a.sgn > 0 ? comp(num, a.num) >= 0 : 1) : (sgn < 0 ? (a.sgn < 0 ? comp(num, a.num) <= 0 : 0) : a.sgn <= 0);}
    inline int operator>=(const int a) {return sgn > 0 ? (a > 0 ? comp(num, a) >= 0 : 1) : (sgn < 0 ? (a < 0 ? comp(num, -a) <= 0 : 0) : a <= 0);}
    inline int operator<(const bignum& a) {return sgn < 0 ? (a.sgn < 0 ? comp(num, a.num) > 0 : 1) : (sgn > 0 ? (a.sgn > 0 ? comp(num, a.num)<0 : 0) : a.sgn>0);}
    inline int operator<(const int a) {return sgn < 0 ? (a < 0 ? comp(num, -a) > 0 : 1) : (sgn > 0 ? (a > 0 ? comp(num, a)<0 : 0) : a>0);}
    inline int operator<=(const bignum& a) {return sgn < 0 ? (a.sgn < 0 ? comp(num, a.num) >= 0 : 1) : (sgn > 0 ? (a.sgn > 0 ? comp(num, a.num) <= 0 : 0) : a.sgn >= 0);}
    inline int operator<=(const int a) {return sgn < 0 ? (a < 0 ? comp(num, -a) >= 0 : 1) : (sgn > 0 ? (a > 0 ? comp(num, a) <= 0 : 0) : a >= 0);}
    inline int operator==(const bignum& a) {return (sgn == a.sgn) ? !comp(num, a.num) : 0;}
    inline int operator==(const int a) {return (sgn*a >= 0) ? !comp(num, ABS(a)) : 0;}
    inline int operator!=(const bignum& a) {return (sgn == a.sgn) ? comp(num, a.num) : 1;}
    inline int operator!=(const int a) {return (sgn*a >= 0) ? comp(num, ABS(a)) : 1;}
    inline int operator[](const int a) {return digit(num, a);}
    friend inline istream& operator>>(istream& is, bignum& a) {read(a.num, a.sgn, is); return is;}
    friend inline ostream& operator<<(ostream& os, const bignum& a) {if(a.sgn < 0)os << '-'; write(a.num, os); return os;}
    friend inline bignum sqrt(const bignum& a) {bignum ret; bignum_t t; memcpy(t, a.num, sizeof(bignum_t)); sqrt(ret.num, t); ret.sgn = ret.num[0] != 1 || ret.num[1]; return ret;}
    friend inline bignum sqrt(const bignum& a, bignum& b) {bignum ret; memcpy(b.num, a.num, sizeof(bignum_t)); sqrt(ret.num, b.num); ret.sgn = ret.num[0] != 1 || ret.num[1]; b.sgn = b.num[0] != 1 || ret.num[1]; return ret;}
    inline int length() {return ::length(num);}
    inline int zeronum() {return ::zeronum(num);}
    inline bignum C(const int m, const int n) {combination(num, m, n); sgn = 1; return *this;}
    inline bignum P(const int m, const int n) {permutation(num, m, n); sgn = 1; return *this;}
};


bignum dp[27][7][155];

bignum Power(bignum x, int n) {
    bignum ret;
    ret = 1;
    while(n--) {
        ret *= x;
    }
    return ret;
}

bignum gcd(bignum a, bignum b) {
    return b == 0 ? a : gcd(b, a % b);
}


int main() {
    int T;
    scanf("%d", &T);
    int n, x;
    for(int t = 1; t <= T; ++t) {
        cin >> n >> x;
        bignum dic;
        dic = 6;
        bignum fm = Power(dic, n);
        for(int i = 1; i <= 6; ++i) {
            dp[1][i][i] = 1;
        }
        for(int i = 2; i <= n; ++i) {
            for(int j = 1; j <= 6; ++j) {
                for(int k = 0; k <= 150; ++k) {
                    dp[i][j][k] = 0;
                    for(int p = 1; p <= 6; ++p) {
                        if(k - j >= 0)dp[i][j][k] += dp[i-1][p][k-j];
                    }
                }
            }
        }
        bignum fz;
        fz=0;
        for(int i = 1; i <= 6; ++i) {
            for(int j = x; j <= 150; ++j) {
                fz += dp[n][i][j];
            }
        }
        bignum g = gcd(fz,fm);
        fz /= g;
        fm /= g;
        printf("Case %d: ",t);
        if(fm==1)cout<<fz<<endl;
        else cout<<fz<<"/"<<fm<<endl;
    }
    return 0;
}