HLG1744组合数学问题与lucas定理运用

The figure below shows Pascal's Triangle:

Baby H divides Pascal's Triangle into some Diagonals, like the following figure:

HLG1744组合数学问题与lucas定理运用

Baby H wants to know the sum of K number in front on the Mth diagonal. Try to calculate it.

Input

There are multiple test cases. The first line is a positive integer T (1<=T<=100) indicating the number of test cases.

For each test case:

Line 1. Two positive integers M and K (1<= M , K <= 100 000).

Output

For each test case, output the sum of K number in front on the Mth diagonal in one line. The answer should modulo to 20 000 003.

Sample Input

2
2 3
3 4

Sample Output

6
20

思路公式，否则超时

C(N,M)+C(N+1,M)+C(N+2,M)==C(N+3,M+1)

代码#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long LL;
LL exp_mod(LL a, LL b, LL p)
{ LL res = 1;
    while(b != 0)
    {
        if(b&1) res = (res * a) % p;
        a = (a*a) % p;
        b >>= 1;
    }
    return res;
}
LL Comb(LL a, LL b, LL p)
{
    if(a < b)   return 0;
    if(a == b) return 1;
    if(b > a - b)   b = a - b; LL ans = 1, ca = 1, cb = 1;
    for(LL i = 0; i < b; ++i)
    {
        ca = (ca * (a - i))%p;
        cb = (cb * (b - i))%p;
    }
    ans = (ca*exp_mod(cb, p - 2, p)) % p;
    return ans;
}

LL Lucas(int n, int m,