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 mod=998244353;
char str[333];
int n,k,dp[333][333][333][2],ans;
void add(int &x,int y)
{
	x+=y;
	if (x>=mod) x-=mod;
}
int main()
{
	scanf("%s",str);
	n=strlen(str);scanf("%d",&k);
	k=min(k,n);str[n]='0';
	dp[0][0][0][0]=1;
	for (int i=0;i<=n;i++)
	{
		for (int j=i;j<=n;j++)
		{
			for (int s=0;s<=k;s++)
			{
				for (int p=0;p<2;p++)
				{
					if (!dp[i][j][s][p]) continue;
					for (int r=0;r<2;r++)
					{
						if (r && p) continue;
						if (str[i]=='0')
						{
							if (!r) add(dp[i+1][j+1][s][0],dp[i][j][s][p]);
							else if (s+1<=k) add(dp[i][j+1][s+1][0],dp[i][j][s][p]);
						}
						else
						{
							if (!r) add(dp[i+1][j][s][1],dp[i][j][s][p]);
							else add(dp[i+1][j+1][s][0],dp[i][j][s][p]);
						}
					}
				}
			}
		}
	}
	for (int i=0;i<=k;i++) 
	{
		add(ans,dp[n][n][i][0]);
		add(ans,dp[n][n][i][1]);
	}
	printf("%d\n",ans);
	return 0;
}