human
You are given a binary string (i. e. a string consisting of characters 0 and/or 1) s of length n. You can perform the following operation with the string s at most once: choose a substring (a contiguous subsequence) of s having exactly k characters 1 in it, and shuffle it (reorder the characters in the substring as you wish).

Calculate the number of different strings which can be obtained from s by performing this operation at most once.

Input

The first line contains two integers n and k (2 ≤ n ≤ 5000.
0 ≤ k ≤ n).

The second line contains the string s of length n, consisting of characters 0 and/or 1.

Output

Print one integer — the number of different strings which can be obtained from s by performing the described operation at most once. Since the answer can be large, output it modulo 998244353.

Examples

Input

7 2
1100110

Output

16

Input

5 0
10010

Output

1

Input

8 1
10001000

Output

10

Input

10 8
0010011000

Output

1

Note

Some strings you can obtain in the first example:

  * to obtain 0110110, you can take the substring from the 1-st character to the 4-th character, which is 1100, and reorder its characters to get 0110.

  * to obtain 1111000, you can take the substring from the 3-rd character to the 7-th character, which is 00110, and reorder its characters to get 11000.

  * to obtain 1100101, you can take the substring from the 5-th character to the 7-th character, which is 110, and reorder its characters to get 101. 


In the second example, k = 0 so you can only choose the substrings consisting only of 0 characters. Reordering them doesn't change the string at all, so the only string you can obtain is 10010.
def m Can you provide a Python program to print one integer — the number of different strings which can be obtained from s by performing the described operation at most once?
assistant
#Here is Python program to print one integer — the number of different strings which can be obtained from s by performing the described operation at most once.
ain():
    n, k = map(int, raw_input().split())
    s = raw_input().strip()
    b = [0] * (n + 1)
    a = []
    for i, x in enumerate(s):
        b[i+1] = b[i]
        if x == '1':
            a.append(i)
            b[i+1] += 1
    a.append(n)
    if b[-1] < k:
        print 1
        return
    mod = 998244353
    f = [1] * (n + 1)
    for i in xrange(2, n + 1):
        f[i] = f[i-1] * i % mod
    invf = [1] * (n + 1)
    invf[-1] = pow(f[-1], mod - 2, mod)
    for i in xrange(n, 1, -1):
        invf[i-1] = invf[i] * i % mod
    def C(N, K):
        if K < 0 or K > N:
            return 0
        return f[N] * invf[K] * invf[N-K] % mod
    ans = 1
    l = len(a)
    for i, x in enumerate(s):
        j = b[i] + k
        if j >= l:
            j = l - 1
        c = j - b[i]
        r = a[j] - i
        if x == '1':
            ans += C(r - 1, c)
            if ans >= mod:
                ans -= mod
        else:
            ans += C(r - 1, c - 1)
            if ans >= mod:
                ans -= mod
    print ans

main()