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 md=998244353;
int f[302][302][702][4],r;
int n,m,i,j,k1,lst,cur,s0,s1;
char s[302];
int main() {
  scanf("%s",s);  n=strlen(s);
  scanf("%d",&m); m=min(m,n);
  f[0][0][0][0]=1;
  for (i=0; i<n; i++) {
    cur=s[i]-'0';
	for (j=0; j<=m; j++) for (k1=0; k1<=i+j; k1++) for (lst=0; lst<4; lst++) if (f[i][j][k1][lst]) {
	  if (cur==0) {
	    f[i+1][j][k1][0]=(f[i+1][j][k1][0]+f[i][j][k1][lst])%md;
		if (lst<2) f[i][j+1][k1+1][1]=(f[i][j+1][k1+1][1]+f[i][j][k1][lst])%md;
	  } else {
	    f[i+1][j][k1][(lst/2)*2+1]=(f[i+1][j][k1][(lst/2)*2+1]+f[i][j][k1][lst])%md;
		if (k1>0 && lst%2==0) f[i+1][j][k1-1][2]=(f[i+1][j][k1-1][2]+f[i][j][k1][lst])%md;
	  }
    }
  }
  for (j=0; j<=m; j++) for (lst=0; lst<4; lst++) r=(r+f[n][j][0][lst])%md;
  printf("%d\n",r);
  return 0;
}