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>
#define MOD 998244353
#define MAXN 307
using namespace std;
long long dp[MAXN][MAXN][MAXN];
int main()
{
	string s; int kt;
	cin>>s>>kt;
	int n=s.size();
	vector<int> nl,sz; nl.push_back(-1); sz.push_back(-1);
	for(int i=0;i<n;i++) if(s[i]=='0') nl.push_back(i);
	nl.push_back(n);
	for(int i=nl.size()-1;i>0;i--) sz.push_back(nl[i]-nl[i-1]-1);
	dp[0][0][0]=1;
	for(int i=1;i<sz.size();i++)
	{
		for(int j=0;j<MAXN;j++) for(int k=0;k<MAXN;k++) for(int t=0;t<=sz[i];t++) if(t<=j && t<=k) dp[i][j][k]=(dp[i][j][k]+dp[i-1][j-t][k-t]);
		for(int j=0;j<MAXN;j++) 
		{
			long long sum=0;
			for(int k=MAXN-1;k>=0;k--)
			{
				dp[i][j][k]=(dp[i][j][k]+sum)%MOD;
				sum=(sum+dp[i-1][j][k])%MOD;
			}
		}
	}
	long long res=0;
	for(int i=0;i<min(MAXN,kt+1);i++) res=(res+dp[sz.size()-1][i][0])%MOD;
	cout<<res;
}