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:
S,K = input().split()
A = list(map(len,S.split("0")))
A[0] = 0
A.append(0)
N = len(A)
K = int(K)
K = min(K,S.count("1"))

MOD = 998244353

dp = [[[0]*(K+1) for _ in [0]*(K+1)] for _ in [0]*N]
dp[-1][0][0] = 1

for i in range(1,N):
    i = N-1-i
    for k in range(K+1):
        for n in range(K+1):
            dp[i][k][n] = sum(dp[i+1][k][n:])%MOD
            for a in range(1,A[i]+1):
                if k-a < 0 or n-a < 0: break
                dp[i][k][n] += dp[i+1][k-a][n-a]
                dp[i][k][n] %= MOD
ans = sum(dp[0][k][0] for k in range(K+1))
ans %= MOD
print(ans)