/******************** 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; }