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;
typedef long long ll;
const int mod = 998244353;
string s;
int k;
int n;
int l[305];
ll mem[305][305][305][2];
ll dp(int id, int rem, int ex, int f){
	if (id == 0) return (ex == 0);
	if (mem[id][rem][ex][f] != -1) return mem[id][rem][ex][f];
	ll res = 0;
	if (s[id-1] == '1'){
		if (rem >= 1) res += dp(id-1,rem-1,ex+1,0);
		if (f == 0) res += dp(l[id],rem,ex,0);
	}
	else if (id == 1 || s[id-2] == '0'){
		res += dp(id-1,rem,ex,0);
		if (ex >= 1) res += dp(id,rem,ex-1,0);
	}
	else {
	    if (f == 0){
            res += dp(id-1,rem,ex,1);
	    }
		if (ex >= 1) res += dp(id,rem,ex-1,1);
		res += dp(l[id],rem,ex,0);
	}
	res %= mod;
	//printf("%d %d %d %lld\n",id,rem,ex,res);
	return mem[id][rem][ex][f] = res;
}
int main(){
	cin >> s >> k;
	n = (int)s.size();
	k = min(k,n);
	memset(mem,-1,sizeof(mem));
	int L = 0;
	for (int i = 1; i <= n; i++){
        l[i] = L;
        if (s[i-1] == '0') L = i;
	}
	printf("%lld",dp(n,k,0,0));

}