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

#import io,os
#input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

M = 998244353

M = 10**9+7

MAXNUM = 100000
factor = [1]*(MAXNUM+2)
factor[-1]=0
storecomb = {}


for i in range(1,MAXNUM+1):
    factor[i] = (factor[i-1]*i)%M

def fastfrac(a,b):
    numb = pow(b,M-2,M)
    return ((a%M)*(numb%M))%M

def comb(n,k):
#    print "*",n,k
    if n<k: return 0
    if n==k: return 1
    if (n,k) in storecomb:  return storecomb[(n,k)]

    num1 = factor[n]
    num2 = factor[k]
    num3 = factor[n-k]
    num = (num2*num3)%M
    output = fastfrac(num1,num)
    storecomb[(n,k)] = output
    return output




def main(t):


    n,k = map(int,input().split())
    s = input()

    if k==0:  
        print(1)
        return 
   








    ones = [-1]

    ans = 1
    for i in range(n):
        if s[i]=='1':
            if len(ones) < k:  
                front = -100 
            else:
                front = ones[-k]
            if front>-100:  ans += comb(i-front-1, k)
        else:
            if len(ones) < k+1: 
                front = -100
            else:
                front = ones[-k-1]
            if front>-100:  ans += comb(i-front-1,k-1)

        ans = ans % M


        if s[i]=='1':  
            ones.append(i)
            
#        print(i,ans)





        
        




    print(ans)




















T = 1 #int(input())
t = 1
while t<=T:
    main(t)
    t += 1
