Problem: Given is a string S consisting of `0` and `1`. Find the number of strings, modulo 998244353, that can result from applying the following operation on S between 0 and K times (inclusive):

* Choose a pair of integers i, j (1\leq i < j\leq |S|) such that the i-th and j-th characters of S are `0` and `1`, respectively. Remove the j-th character from S and insert it to the immediate left of the i-th character.

Constraints

* 1 \leq |S| \leq 300
* 0 \leq K \leq 10^9
* S consists of `0` and `1`.

Input

Input is given from Standard Input in the following format:


S K


Output

Find the number of strings, modulo 998244353, that can result from applying the operation on S between 0 and K times (inclusive).

Examples

Input

0101 1


Output

4


Input

01100110 2


Output

14


Input

1101010010101101110111100011011111011000111101110101010010101010101 20


Output

113434815

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
const ll mod = 998244353;

int main(){
  string s;
  int k;
  cin >> s >> k;
  vector<int> v;
  bool f = false;
  int p = 0;
  int one = 0;
  rep(i,s.length()) {
    if(s[i] == '0') {
      f = true;
      v.push_back(p);
      p = 0;
    } else {
      one++;
      p++;
    }
  }
  if(p > 0) v.push_back(p);
  if(!f) {
    cout << 1 << endl;
    return 0;
  }
  int l = v.size();
  k = min(k,300);
  vector<vector<vector<ll>>> dp(l+1,vector<vector<ll>>(k+1,vector<ll>(k+1)));
  dp[0][0][0] = 1;
  reverse(v.begin(),v.end());
  rep(i,l) {
    rep(j,k+1) {
      rep(a,k+1) {
        rep(b,a+1) (dp[i+1][j][b] += dp[i][j][a]) %= mod; 
      }
    }
    rep(j,k+1) {
      rep(a,k+1) {
        for(int b = 1; b <= v[i]; b++) {
          if(a+b <= k and j+b <= k) (dp[i+1][j+b][a+b] += dp[i][j][a]) %= mod;
        }
      }
    }
  }
  ll ans = 0;
  rep(i,k+1) (ans += dp[l][i][0]) %= mod;
  cout << ans << endl;
  return 0;
}