There are NN different kinds of transport ships on the port. The i^{th}ith kind of ship can carry the weight of V[i]V[i] and the number of the i^{th}ith kind of ship is 2^{C[i]} - 12C[i]?1. How many different schemes there are if you want to use these ships to transport cargo with a total weight of SS?

It is required that each ship must be full-filled. Two schemes are considered to be the same if they use the same kinds of ships and the same number for each kind.

Input

The first line contains an integer T(1 \le T \le 20)T(1≤T≤20), which is the number of test cases.

For each test case:

The first line contains two integers: N(1 \le N \le 20), Q(1 \le Q \le 10000)N(1≤N≤20),Q(1≤Q≤10000), representing the number of kinds of ships and the number of queries.

For the next NN lines, each line contains two integers: V[i](1 \le V[i] \le 20), C[i](1 \le C[i] \le 20)V[i](1≤V[i]≤20),C[i](1≤C[i]≤20), representing the weight the i^{th}ith kind of ship can carry, and the number of the i^{th}ith kind of ship is 2^{C[i]} - 12C[i]?1.

For the next QQ lines, each line contains a single integer: S(1 \le S \le 10000)S(1≤S≤10000), representing the queried weight.

Output

For each query, output one line containing a single integer which represents the number of schemes for arranging ships. Since the answer may be very large, output the answer modulo 10000000071000000007.

樣例輸入復制

1
1 2
2 1
1
2

樣例輸出復制

0
1

題目來源

ACM-ICPC 2018 焦作賽區網絡預賽

題解：二進制求和+DP

參考代碼：

#include<iostream>
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<string>
#include<algorithm>
#include<bitset>
#define INF 0x3f3f3f3f
#define clr(x, y) memset(x, y, sizeof(x))
#define mod 1000000007
using namespace std;
typedef long long LL;
const int maxn=25;
const int maxm=10010;
int v[maxn],c[maxn];
LL dp[maxm];

int main()
{
    int t;
    scanf("%d", &t);
    while(t--)
    {
        int n, q;
        scanf("%d%d", &n, &q);
        memset(dp, 0, sizeof(dp));
        dp[0] = 1;
        for(int i = 1; i <= n; i++)
        {
            scanf("%d%d", &v[i], &c[i]);
            LL cur = 1;
            for(int j = 1; j <= c[i]; j++)
            {
                for(int k = 10000; k >= cur * v[i]; k--)
                    dp[k] = (dp[k] + dp[k - cur * v[i]]) % mod;
                cur<<=1;
            }
        }
        for(int i = 1; i <= q; i++)
        {
            int s;
            scanf("%d", &s);
            printf("%lld\n", dp[s]);
        }
    }
    return 0;
}

ACM-ICPC 2018 焦作賽區網絡預賽 K題 Transport Ship