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;
typedef long long ll;
char s[305];
int n,m,k,a[305],b[305];
ll d[305][305][305],ans,mod = 998244353;

int main() {
    ios_base::sync_with_stdio(false); cin.tie(0);
    cin >> s+1 >> k;
    m = strlen(s+1);
    n = 1;
    for(int i = 1;i <= m;i++) {
        if(s[i] == '0') n++;
        else a[n]++;
    }
    n++;
    for(int i = n-1;i >= 0;i--) {
        b[i] = b[i+1]+a[i];
    }

    k = min(b[1],k);
    d[0][0][0] = 1;
    for(int i = 1;i <= n;++i) {
        for(int c = 0;c <= a[i];c++) {
            for(int j = c;j <= k;j++) {
                for(int l = j;l <= k;l++) {
                    d[i][l][j-c] = (d[i][l][j-c]+d[i-1][l][j])%mod;
                }
            }
        }
        for(int c = 1;c <= k;++c) {
            for(int j = k-c;j >= 0;j--) {
                for(int l = 0;l <= j;l++) {
                    d[i][j+c][l+c] = (d[i][j+c][l+c]+d[i-1][j][l])%mod;
                }
            }
        }
    }
    for(int i = 0;i <= k;i++) ans += d[n][i][0];
    cout << ans%mod;
}