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.
5 2
00011
 5 4
11011
 81 5
100000101000000011001101010100001010111000000110000000001000101101111000001000110
 4 3
1011
 47 25
11110011111001110100101010011000110111011011101
 291 159
011001110111110110001111000110001001111100010001011000110100110010001101100110111010101111100111110000110111001100111010001000011001010011011100101000101011010110010011010100100101111010111000001011110101001011101110100100111110011001101010001110110101010101100011101110111000011111011001110
 459 15
101010101010101010101010101010101010101010101111111111111111111111010101010101010101010101011111111111111111111101010101010101010101111111111111111111111101010101010101010111111111111111111111111101010101010101111111111111111111111111110110101010101011111111111111111111111111111001000111111111111111111111111111110000011111111111111111111111111111000001111111111111111111111111111100001111111111111111111111111111100111111111111111111111111111110111111111111
 105 58
110101000111100000011011011101110100001000110011010101100010111001011111010010111101011011010110011011110
 52 11
0110011111001000010000100010010001010100000100110100

10
 5
 187538
 4
 314445058
 1
 0
 132732930
 478323746

def main():
    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()
