1049 - Deg-route

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;

#include <iostream>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <string>
const LL MOD = 1e4 + 7;
LL quick_pow (LL a,LL b,LL MOD) {
    //求解 a^b%MOD的值
    LL base=a%MOD;
    LL ans=1; //相乘，所以这里是1
    while (b) {
        if (b&1) {
            ans=(ans*base)%MOD; //如果这里是很大的数据，就要用quick_mul
        }
        base=(base*base)%MOD;    //notice
        //注意这里,每次的base是自己base倍
        b>>=1;
    }
    return ans;
}

LL C (LL n,LL m,LL MOD) {
    if (n<m) return 0; //防止sb地在循环，在lucas的时候
    if (n==m) return 1;
    LL ans1 = 1;
    LL ans2 = 1;
    LL mx=max(n-m,m); //这个也是必要的。能约就约最大的那个
    LL mi=n-mx;
    for (int i = 1; i <= mi; ++i) {
        ans1 = ans1*(mx+i)%MOD;
        ans2 = ans2*i%MOD;
    }
    return (ans1*quick_pow(ans2,MOD-2,MOD)%MOD); //这里放到最后进行,不然会很慢
}
LL Lucas (LL n,LL m,LL MOD) {
    LL ans=1;
    while (n && m && ans) {
        ans=ans*C(n%MOD,m%MOD,MOD)%MOD;
        n /= MOD;
        m /= MOD;
    }
    return ans;
}
LL calc(LL x, LL y) {
    LL ans = (Lucas(2 * x, x, MOD) + MOD - Lucas(2 * x, x + 1, MOD)) % MOD;
    return ans;
}
void work() {
    LL x, y;
    cin >> x >> y;
    if (y == 0) {
        cout << 1 << endl;
    } else {
        if (x == y) {
            cout << calc(x, y) << endl;
        } else {
            cout << (Lucas(x + y, y, MOD) - Lucas(x + y, y - 1, MOD) + MOD) % MOD << endl;
        }
    }
}
int main() {
#ifdef local
    freopen("data.txt","r",stdin);
#endif
//    for (x = 1; x <= 10; ++x) {
//        for (y = 0; y <= x; ++y) {
//            work();
//        }
//        cout << endl;
//    }
    IOS;
    int t;
    cin >> t;
    while (t--) work();

    return 0;
}