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
input = stdin.readline


mod = 998244353
def add(a , b):return ((a%mod) + (b%mod))%mod
def sub(a , b):return (a - b + mod)%mod
def mul(a , b):return ((a%mod) * (b%mod))%mod
def div(a , b):return mul(a , pow(b , mod - 2 , mod))

size = 5001
fact , facti = [1] , [1]
for i in range(1 , size):
    fact.append(mul(fact[-1] , i))
    facti.append(pow(fact[-1] , mod - 2 , mod))


def get(n , x , y):

    ans = mul(fact[n] , mul(facti[x] , facti[y]))
    return ans

def answer():
   
    ans , prevupper , i = 0 , [-1] , 0
    for i in range(n):

        count , upper = 0 , -1
        for j in range(i , n):
            if(a[j] == '1'):count += 1
            if(count == (k + 1)):
                upper = j - 1
                break

        if(count == k):upper = n - 1
        if(upper == -1):break

        ans = add(ans , get(upper - i + 1 , k , (upper - i + 1) - k))

        if(prevupper[-1] > i):

            x , y = 0 , 0
            for j in range(i , prevupper[-1] + 1):
                x += (a[j] == '1')
                y += (a[j] == '0')
            
            ans = sub(ans , get(prevupper[-1] - i + 1 , x , y))


        prevupper.append(upper)

    if(ans == 0):return 1
    return ans
        

for T in range(1):

    n , k = map(int,input().split())
    a = input().strip()
    
    print(answer())
