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 MAX = 510000;
const int MOD = 998244353;

     signed main(){
       string s;int K;
       cin>>s>>K;
       vector<int> c;
       c.push_back(0);int t=0;
       for(auto&&i :s){
          if(i=='0')c.push_back(0);
          else {c[c.size()-1]++;t++;}
       }
       int dp[c.size()+1][t+1][301];
       for(int i=0;i<=t;i++)fill(dp[0][i],dp[0][i]+301,0);
       dp[0][0][0]=1;int o=0;
       for(int i=1;i<=c.size();i++){
          o+=c[i-1];
             for(int j=0;j<=t;j++)fill(dp[i][j],dp[i][j]+301,0);
          for(int j=0;j<=t;j++)for(int k=0;k<301;k++)for(int j2=0;j2<=j;j2++)if(k-max(j-j2-c[i-1],0ll)>=0&&j>=o)dp[i][j][k]=(dp[i][j][k]+dp[i-1][j2][k-max(j-j2-c[i-1],0ll)])%MOD;
       }
   int ans=0;
   for(int i=0;i<=min(K,300ll);i++){ans=(ans+dp[c.size()][t][i])%MOD;}//cerr<<dp[c.size()][t][i]<<endl;}
   
cout<<ans<<endl;


     }