2018 Multi-University Training Contest 8

#include <iostream>
#include <cstdio>
#include <cstdlib>
using namespace std;
const int MAX=3e5+5;
const long long mod=998244353;
long long fac[MAX],rev[MAX];
long long qp(long long p,long long q)
{
    int cnt=1;
    while(q>0)
    {
        if(q%2==1) cnt=(cnt*p)%mod;
        q/=2;
        p=(p*p)%mod;
    }
    return cnt%mod;
}

long long C(long long a,long long b)
{
    if(a<0||b<0) return 0;
    long long flag=fac[a];
    return ((fac[a]*rev[b])%mod*rev[a-b])%mod;
}

long long n,m,k;

long long solve(long long sum,long long num,long long p)
{
    if(sum==0) return 1;
    long long cnt=0;
    int i,j;
    for(i=0;i<=num;i++)
    {
        long long a=C(num,i),b=C(sum-p*i-i+num-1,sum-p*i-i);
        long long flag=(C(num,i)*C(sum-p*i-i+num-1,sum-p*i-i))%mod;
        if(i%2==1) flag=(mod-flag)%mod;
        cnt=(cnt+flag)%mod;
    }
    return cnt;
}

int main()
{
    int i,j;
    int t;
    scanf("%d",&t);
        fac[0]=1;
    rev[0]=1;
    for(i=1;i<MAX;i++)
    {
        fac[i]=(fac[i-1]*i)%mod;
        rev[i]=qp(fac[i],mod-2);
    }
    while(t--){
        scanf("%lld%lld%lld",&n,&m,&k);
        long long ans=solve(k,m,n-1);
        printf("%lld\n",ans);
    }

    return 0;
}