整数拆分

知识点：母函数（其实更建议去看《组合数学》），五边形数定理（百度总结的也不错）。

#include<bits/stdc++.h>
#define ll long long
#define P pair<int,int>
#define pb push_back
#define lson root << 1
#define INF (int)2e9 + 7
#define maxn (int)1e5 + 7
#define rson root << 1 | 1
#define LINF (unsigned long long int)1e18
#define mem(arry, in) memset(arry, in, sizeof(arry))
using namespace std;

const int mod = (int)1e9 + 7;

int T, n, k;
int dp[maxn];

void Inite(){
    mem(dp, 0);
    dp[0] = 1;
    for(int i = 1; i <= 100000; i++){
        for(int j = 1, r = 1; i - (3 * j * j - j) / 2 >= 0; j++, r *= -1){
            dp[i] += dp[i - (3 * j * j - j) / 2] * r;
            dp[i] %= mod;
            dp[i] =(dp[i] + mod) % mod;
            if(i - (3 * j * j + j) / 2 >= 0){
                dp[i] += dp[i - (3 * j * j + j) / 2] * r;
                dp[i] %= mod;
                dp[i] =(dp[i] + mod) % mod;
            }
        }
    }
}

int main()
{
    Inite();
    cin >> T;
    while(T--){
        cin >> n >> k;
        cout << (dp[n] - dp[n - k] + mod) % mod << endl;
    }
    return 0;
}