记录编号	590790	评测结果	AAAAA
题目名称	[HSOI 2020] UNO	最终得分	100
用户昵称	┭┮﹏┭┮	是否通过	通过
代码语言	C++	运行时间	2.440 s
提交时间	2024-07-11 16:08:50	内存使用	49.29 MiB

#include <bits/stdc++.h> 
using namespace std;
#define ll long long
const int N = 3e6+10;
const ll mod = 998244353;

ll read(){
    ll x = 0,f = 1;char c = getchar();
    for(;c < '0' || c > '9';c = getchar())if(c == '-')f = -1;
    for(;c >= '0' && c <= '9';c = getchar())x = (x<<1) + (x<<3) + c-'0';
    return x * f;
}

int n,m,k;
ll f[N] = {1,1},inv[N] = {1,1},ans = 0;

ll ksm(ll x,ll y){
    ll ans = 1;
    while(y){
        if(y & 1)ans = ans * x % mod;
        x = x * x % mod,y >>= 1;
    }return ans;
}
ll C(ll x,ll y){
    if(x < 0 || y < 0 || x - y < 0)return 0;
    return f[x] * inv[y] % mod * inv[x-y] % mod;
}
int main(){
    freopen("UNO.in","r",stdin);
    freopen("UNO.out","w",stdout);
    n = read(),m = read(),k = read();
    for(int i = 2;i <= 3e6;i++)f[i] = f[i-1] * i % mod,inv[i] = ksm(f[i],mod-2);
    for(int i = 1;i <= n;i++){
        (ans += C(n-1,i-1) * C(m-1,i-2) % mod * C(2*i,k-n-m-1+2*i) % mod) %= mod;
        (ans += 2ll * C(n-1,i-1) % mod * C(m-1,i-1) % mod * C(2*i+1,k-n-m+2*i) % mod) %= mod;
        (ans += C(n-1,i-1) * C(m-1,i) % mod * C(2*i+2,k-n-m+1+2*i) % mod) %= mod;
    }
    printf("%lld\n",ans);

    
    return 0;
    
}