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

from sys import stdin, stdout

N = 998244353

def egcd(a, b):
    """return (g, x, y) such that a*x + b*y = g = gcd(a, b)"""
    if a == 0:
        return (b, 0, 1)
    else:
        g, y, x = egcd(b % a, a)
        return (g, x - (b // a) * y, y)

def modinv(a, m = N):
    """return inverse of a mod m"""
    g, x, y = egcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

fact = [1]
invfact = [1]

for i in range(1,5001):
    fact.append((fact[-1]*i)%N)
    invfact.append((invfact[-1]*modinv(i))%N)

n, k = [int(x) for x in stdin.readline().split()]
s = stdin.readline().strip()

locations = []

for i in range(n):
    if s[i] == '1':
        locations.append(i)

if k == 0 or len(locations) < k:
    stdout.write('1\n')

else:
    answer = 0
    for i in range(len(locations)-k+1):
        if i == 0:
            lower = 0
        else:
            lower = locations[i-1]+1

        if i == len(locations)-k:
            upper = n-1
        else:
            upper = locations[i+k]-1

        answer = (answer + fact[upper-lower+1]*invfact[k]*invfact[upper-lower+1-k])%N

    for i in range(len(locations)-k):
        lower = locations[i]+1
        upper = locations[i+k]-1
        answer = (answer - fact[upper-lower+1]*invfact[k-1]*invfact[upper-lower+1-k+1])%N

    stdout.write(str(answer)+'\n')
