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 sys
infile = sys.stdin.buffer
def gs()  : return infile.readline().rstrip()
def gi()  : return int(gs())
def gss() : return gs().split()
def gis() : return [int(x) for x in gss()]
MOD = 998244353

N = 10000
pw =[1 for i in range(N + 1)]
for i in range(1, len(pw)):
    pw[i] *= pw[i-1]
    pw[i] *= 2
    pw[i] %= MOD

fact =[i for i in range(N + 1)]
fact[0] = 1
for i in range(2, len(fact)):
    fact[i] *= fact[i-1]
    fact[i] %= MOD
factinv = [1 for _ in range(len(fact))]




factinv[len(fact)-1] = pow(fact[len(fact)-1], MOD-2,MOD) 
for ii in range(len(fact)-2,-1,-1):
    factinv[ii] = factinv[ii+1] * (ii+1)
    factinv[ii] %= MOD

def nCr(n,r):return (fact[n] * factinv[r] * factinv[n-r]) % MOD


def f(a,k):
    if k == 0:
        return 1
    ans = 1
    a = list(map(int, str(a)))
    
    if sum(a) < k:
    
        return ans
    t = [0 for _ in range(len(a))]
    for i in range(len(t)):
        t[i] += a[i]
        t[i] += t[i-1] if (i-1 >= 0) else 0

    for i in range(len(a)):
        for j in range(i+1,len(a)):
            if t[j] - (t[i-1] if i-1>=0 else 0) <= k:
                ones = t[j] - (t[i-1] if i-1>=0 else 0)
                total = j - i + 1 -2
                if a[i] == 0:
                    ones -=1
                if a[j] == 0:
                    ones -=1
                if (total >= 0) and (ones>= 0) and (ones <= total) :
                    ans += nCr(total, ones)
    return ans


    


def main(infn="") :
    global infile
    infile = open(infn,"r") if infn else open(sys.argv[1],"r") if len(sys.argv) > 1 else sys.stdin
    ###################################################################
        
    cs = 1#gi()    
    for case in range(1, cs+1):
        n,k = gis()
        print (f(gs(),k))
    ###################################################################    
if __name__ == '__main__' : main()