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 int long long

const int mod=998244353,N=305;
int dp[N][N][N];

int32_t main(){
    ios::sync_with_stdio(0),cin.tie(0);
    string st;
    int k;
    cin >> st >> k;
    reverse(st.begin(),st.end());
    st+='0';
    vector <int> v;
    int c=0;
    v.push_back(-1);
    for(int i=0;i<st.size();i++){
        if(st[i]=='0'){
            v.push_back(c);
            c=0;
        }
        else c++;
    }
    k=min(k,(int)st.size());
    int m=(int)v.size()-1;
    dp[0][0][0]=1;
    for(int i=1;i<=m;i++){
        for(int x=0;x<N;x++){
            for(int j=N-2;j>=0;j--)
                dp[i][j][x]=(dp[i-1][j][x]+dp[i][j+1][x])%mod;
        }
        for(int y=1;y<=v[i];y++){
            for(int x=0;x<N;x++){
                for(int j=0;j<N;j++){
                    if(j-y<0 or x-y<0)continue;
                    dp[i][j][x]=(dp[i][j][x]+dp[i-1][j-y][x-y])%mod;
                }
            }
        }
    }
    int ans=0;
    for(int i=0;i<=k;i++)
        ans=(ans+dp[m][0][i])%mod;
    cout << ans;
}