https://www.luogu.com.cn/problem/solution/P4345

#include<bits/stdc++.h>   // by: hansang
using namespace std;
typedef long long LL;
const LL P=2333;
const int N=2333+10;
LL f[N][N], c[N][N];
LL Lucas(LL n, LL m)
{
    if((m==0) || (n==m)) return 1;
    else if(n<m) return 0;
    else return c[n%P][m%P]*Lucas(n/P, m/P)%P;
}
LL F(LL n, LL m)
{
    if(m<0) return 0;
    else if(n==0 || m==0) return 1;
    else if(n<P && m<P) return f[n][m];
    else return (f[n%P][P-1]*F(n/P, m/P-1)+f[n%P][m%P]*Lucas(n/P, m/P))%P;
}
int main()
{
    int T; scanf("%d", &T); 
    memset(c, 0, sizeof(c)); memset(f, 0, sizeof(f));
    for(int i=0; i<=N-10; i++) c[i][i]=c[i][0]=1, f[i][0]=1;
    for(int i=1; i<=N-10; i++) for(int j=1; j<=N-10; j++) c[i][j]=(c[i-1][j-1]+c[i-1][j])%P;
    for(int i=0; i<=N-10; i++) for(int j=1; j<=N-10; j++) f[i][j]=(f[i][j-1]+c[i][j])%P;
    while(T--)
    {
        LL n, m; scanf("%lld%lld", &n, &m);
        printf("%lld\n", F(n, m));
    }
    return 0;
}

https://www.luogu.com.cn/problem/solution/P4345

#include<bits/stdc++.h>   // by: hansang
using namespace std;
typedef long long LL;
const LL P=2333;
const int N=2333+10;
LL f[N][N], c[N][N];
LL Lucas(LL n, LL m)
{
    if((m==0) || (n==m)) return 1;
    else if(n<m) return 0;
    else return c[n%P][m%P]*Lucas(n/P, m/P)%P;
}
LL F(LL n, LL m)
{
    if(m<0) return 0;
    else if(n==0 || m==0) return 1;
    else if(n<P && m<P) return f[n][m];
    else return (f[n%P][P-1]*F(n/P, m/P-1)+f[n%P][m%P]*Lucas(n/P, m/P))%P;
}
int main()
{
    int T; scanf("%d", &T); 
    memset(c, 0, sizeof(c)); memset(f, 0, sizeof(f));
    for(int i=0; i<=N-10; i++) c[i][i]=c[i][0]=1, f[i][0]=1;
    for(int i=1; i<=N-10; i++) for(int j=1; j<=N-10; j++) c[i][j]=(c[i-1][j-1]+c[i-1][j])%P;
    for(int i=0; i<=N-10; i++) for(int j=1; j<=N-10; j++) f[i][j]=(f[i][j-1]+c[i][j])%P;
    while(T--)
    {
        LL n, m; scanf("%lld%lld", &n, &m);
        printf("%lld\n", F(n, m));
    }
    return 0;
}