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

# cook your dish here
import sys
#import random
from bisect import bisect_left as lb
from bisect import bisect_right as rb
from collections import deque
#sys.setrecursionlimit(10**8)
from queue import PriorityQueue as pq
from math import gcd
#import math
input_ = lambda: sys.stdin.readline().strip("\r\n")
ii = lambda : int(input_())
il = lambda : list(map(int, input_().split()))
ilf = lambda : list(map(float, input_().split()))
lii = lambda : list(map(int, list(ip())))
ip = lambda : input_()
fi = lambda : float(input_())
ap = lambda ab,bc,cd : ab[bc].append(cd)
li = lambda : list(input_())
pr = lambda x : print(x)
prinT = lambda x : print(x)
f = lambda : sys.stdout.flush()
inv =lambda x:pow(x,mod-2,mod)
dx = [0,0,1,-1]
dy = [1,-1,0,0]
mod = 10**9 + 7
mod1 = 998244353

fact = [1]

for i in range (1,10005) :
    fact.append((fact[-1]*i)%mod1)

inv = [pow(fact[-1],mod1-2,mod1)]

for i in range (10004,0,-1) :
    inv.append((inv[-1]*i)%mod1)

inv.reverse()

n,k = il()
s = list(ip())

if (k == 0) :
    print(1)
    exit(0)


ans = 0

for i in range (n) :
    x,y = 0,0
    if (s[i] == '1') :
        lo = i
        hi = i
        for j in range (i,n) :
            if (s[j] == '1') : 
                x += 1
                if (x > k) :
                    hi = j-1
                    x-=1
                    break
            else :
                y += 1

        for j in range (i-1,-1,-1) :
            if (s[j] == '1') :
                lo = j + 1
                break
            y += 1
        if (x == k) :
            ans += (fact[x+y]*inv[x]*inv[y])%mod1
            ans = (ans + mod1 - 1) %mod1

if (k == 1) :
    print(ans + 1)
    exit(0)

k -= 1
    
ans1 = ans

ans = 0

fi = -1
la = -1

for i in range (n) :
    if (s[i] == '1') :
        fi = i
        break

for i in range (n-1,-1,-1) :
    if (s[i] == '1') :
        la = i
        break

for i in range (n) :
    x,y = 0,0
    if (s[i] == '1' and i != fi and i != la) :
        lo = i
        hi = i
        for j in range (i,n) :
            if (s[j] == '1') : 
                x += 1
                if (x > k) :
                    hi = j-1
                    x-=1
                    break
            else :
                y += 1

        for j in range (i-1,-1,-1) :
            if (s[j] == '1') :
                lo = j + 1
                break
            y += 1
        if (x == k) :
            ans += (fact[x+y]*inv[x]*inv[y])%mod1
            ans = (ans + mod1 - 1) %mod1

ans = (ans1 + mod1 - ans)%mod1

print((ans+1)%mod1)
        
        
