output_description: Print the number of the ways to paint tiles, modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N A B K
attempt: #include <bits/stdc++.h>
  using namespace std;
  
  typedef long long ll;
  
  const ll MOD = 998244353;
  
  ll ncr[300005];
  ll fact[300005];
  ll inv[300005];
  
  ll ex(ll a, ll b)
  {
  	if (b == 0) return 1;
  	ll r = ex(a, b>>1);
  	r *= r; r %= MOD;
  	if (b&1) r = (r*a)%MOD;
  	return r;
  }
  
  int main()
  {
  	ll n, a, b, k, ans = 0;
  	cin >> n >> a >> b >> k;
  
  	fact[0] = 1; inv[0] = 1;
  	for (ll i = 1;i <= n;i++)
  	{
  		fact[i] = fact[i-1]*i; fact[i] %= MOD;
  		inv[i] = ex(fact[i], MOD-2);
  	}
  	for (ll i = 0;i <= n;i++)
  	{
  		ncr[i] = fact[n]*inv[i];
  		ncr[i] %= MOD;
  		ncr[i] *= inv[n-i];
  		ncr[i] %= MOD;
  	}
  
  	for (ll i = 0;i <= n;i++)
  	{
  		ll rem = k-i*a;
  		if (rem >= 0 && rem%b == 0)
  		{
  			ans += ncr[i]*ncr[rem/b];
  			ans %= MOD;
  		}
  	}
  	cout << ans << endl;
  	return 0;
  }
  
problem_description: Statement
  
  Takahashi has a tower which is divided into N layers. Initially, all the
  layers are uncolored. Takahashi is going to paint some of the layers in red,
  green or blue to make a beautiful tower. He defines the _beauty of the tower_
  as follows:
  
    * The beauty of the tower is the sum of the scores of the N layers, where the score of a layer is A if the layer is painted red, A+B if the layer is painted green, B if the layer is painted blue, and 0 if the layer is uncolored.
  
  Here, A and B are positive integer constants given beforehand. Also note that
  a layer may not be painted in two or more colors.
  
  Takahashi is planning to paint the tower so that the beauty of the tower
  becomes exactly K. How many such ways are there to paint the tower? Find the
  count modulo 998244353. Two ways to paint the tower are considered different
  when there exists a layer that is painted in different colors, or a layer that
  is painted in some color in one of the ways and not in the other.
samples: [{"input": "4 1 2 5", "output": "40\n    \n\nIn this case, a red layer worth 1 points, a green layer worth 3 points and the\nblue layer worth 2 points. The beauty of the tower is 5 when we have one of\nthe following sets of painted layers:\n\n  * 1 green, 1 blue\n  * 1 red, 2 blues\n  * 2 reds, 1 green\n  * 3 reds, 1 blue\n\nThe total number of the ways to produce them is 40.\n\n* * *"}, {"input": "2 5 6 0", "output": "1\n    \n\nThe beauty of the tower is 0 only when all the layers are uncolored. Thus, the\nanswer is 1.\n\n* * *"}, {"input": "90081 33447 90629 6391049189", "output": "577742975"}]