提出 #75874051

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ソースコード 拡げる

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define all(x) (x).begin(), (x).end()
#define pb push_back

template<class T> inline bool chmax(T& a, T b) { return a < b ? a = b, 1 : 0; }
template<class T> inline bool chmin(T& a, T b) { return a > b ? a = b, 1 : 0; }

const int MOD =  
998244353;
// combinatorics:

const int MAXN = 3e6 + 5;

long long fact[MAXN], invFact[MAXN];

long long modpow(long long a, long long b) {
    long long res = 1;

    while (b) {
        if (b & 1)
            res = (res * a) % MOD;

        a = (a * a) % MOD;
        b >>= 1;
    }

    return res;
}

void initCombinatorics() {
    fact[0] = 1;

    for (int i = 1; i < MAXN; i++)
        fact[i] = (fact[i - 1] * i) % MOD;

    invFact[MAXN - 1] = modpow(fact[MAXN - 1], MOD - 2);

    for (int i = MAXN - 2; i >= 0; i--)
        invFact[i] = (invFact[i + 1] * (i + 1)) % MOD;
}

long long nCr(int n, int r) {
    if (r < 0 || r > n)
        return 0;

    return fact[n] * invFact[r] % MOD * invFact[n - r] % MOD;
}

long long nPr(int n, int r) {
    if (r < 0 || r > n)
        return 0;

    return fact[n] * invFact[n - r] % MOD;
}
void solve() {
    
    int x1,x2,x3;cin>>x1>>x2>>x3;
    // 1 can come only negihtbouring 1 and 2;
    // same for 2 and 3 , 
    // most flexible 2 ;
    // 1 and 3 cant be neighbour

    // gaps = 2 +1;
    int gaps=x2+1;
    ll ans=0;
    for(int i=1;i<=min(gaps,x1);i++){
        

        ll choose1=nCr(gaps,i);
        ll put1=nCr(x1-1,i-1);
        ll put3=nCr(gaps-i+x3-1,x3);

        ll curr=choose1*put1%MOD;
        curr=(curr*put3)%MOD;
        ans=(ans+curr)%MOD;
    }
    cout<<ans<<'\n';

    
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int tt = 1;
    //cin >> tt;
    initCombinatorics();

    while (tt--) {
        solve();
    }

    return 0;
}

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