Submission #3786220

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Source Code Expand

/**
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*/
#include <cstring>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <queue>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cassert>

#define F first
#define S second
#define endl '\n'
#define deb(x) cout<<#x<<' '<<x<<endl;
#define pb push_back

/*
#ifdef IZI_KATKA
#define int __int64_t
#else
#define int __int64
#endif
*/

const long long MOD = 998244353;
const long long MAXN = 1e6 + 1;
using namespace std;

typedef long long ll;

long long readInt() {
    bool minus1 = false;
    long long result = 0;
    char ch;
    ch = getchar();
    while (true) {
        if (ch == '-') break;
        if (ch >= '0' && ch <= '9') break;
        ch = getchar();
    }
    if (ch == '-') minus1 = true; else result = ch-'0';
    while (true) {
        ch = getchar();
        if (ch < '0' || ch > '9') break;
        result = result*10 + (ch - '0');
    }
    if (minus1)
        return -result;
    else
        return result;
}

ll fact[MAXN];


ll binpow (ll a, ll n) {
	if (n == 0)
		return 1;
	if (n % 2 == 1)
		return (binpow (a, n-1) * a) % MOD;
	else {
		ll b = binpow (a, n/2) % MOD;
		return (b * b) % MOD;
	}
}


ll C(ll n, ll k) {
	ll res1 = fact[n];
	ll res2 = (fact[k] * fact[n - k]) % MOD;
	return (res1 * binpow(res2, MOD - 2)) % MOD;
}

int main() {
	#ifdef IZI_KATKA
	assert(freopen("input", "r", stdin));
    assert(freopen("output", "w", stdout));
    #endif
    ll N = readInt(), A = readInt(), B = readInt(), K = readInt();
    fact[0] = 1;
    for (int i = 1; i <= N; i++) {
    	fact[i] = fact[i - 1] * i;
    	fact[i] %= MOD;
    }
    ll ans = 0;
    for (int cnt1 = 0; cnt1 <= N; cnt1 ++) {
		ll res = cnt1 * A;
		if (K - res < 0) continue;
		if ((K - res) % B == 0) {
			ll cnt2 = (K - res) / B;
			if (cnt2 <= N)
			ans += C(N, cnt1) * C(N, cnt2);
			ans %= MOD;
		}  
    }
    cout << ans;
    return 0;
}

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