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;
const int maxn = 305;
const int mod = 998244353;
vector <int> v;
int mem[2][maxn][maxn][maxn];
int N, K;

int dp(int state, int cur, int moves, int need) {
  if(moves > K || moves > N) return 0;
  if(cur == v.size()) {
    return need == 0;
  }
  int &ans = mem[state][cur][moves][need];
  if(ans != -1) return ans;
  ans = dp(0, cur + 1, moves, need);
  if(state == 0) {
    ans += dp(1, cur, moves + 1, need + 1);
    ans %= mod;
    for(int i = 1; i <= v[cur] && i <= need; i++) {
      ans += dp(0, cur + 1, moves, need - i);
      ans %= mod;
    }
  } else {
    ans += dp(1, cur, moves + 1, need + 1);
    ans %= mod;
  }
  return ans;
}
int main() {
  string s;
  cin >> s >> K;
  N = s.size();
  int cnt = 0;
  for(auto i : s) {
    if(i == '0') {
      v.push_back(cnt);
      cnt = 0;
    }
    else cnt = cnt + 1;
  }
  v.push_back(cnt);
  memset(mem, -1, sizeof mem);
  cout << dp(0, 0, 0, 0) << endl;
  return 0;
}