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 PYTHON3):

Solution:
mod = 998244353
S,K = input().split()
a = []
c = 0
for i in range(len(S)):
    if S[i]=='0':
        a.append(c)
        c = 0
    else:
        c += 1
if S[-1]=='1':
    a.append(c)
a = a[::-1]
K = min(sum(a),int(K))
N = len(a)
dp = [[[0]*(K+1) for _ in range(K+1)] for _ in range(N+1)]
dp[0][0][0] = 1
for i in range(N):
    for j in range(K+1):
        for k in range(j+1):
            for l in range(a[i]+1):
                if j+l>K:
                    break
                dp[i+1][j+l][k+l] += dp[i][j][k]
                dp[i+1][j+l][k+l] %= mod
            for l in range(1,k+1):
                dp[i+1][j][k-l] += dp[i][j][k]
                dp[i+1][j][k-l] %= mod
                
ans = 0
for k in range(K+1):
    ans += dp[N][k][0]
    ans %= mod
print(ans)