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)


s = ['#'] + s

pre = [0 for i in range (n+2)]
suf = [0 for i in range (n+2)]
ch = [[0,0] for i in range (n+1)]

c = 0

for i in range (1,n+1) :
    ch[i] = ch[i-1].copy()

    t = 0
    if (s[i] == '1') :
        t = 1
    
    ch[i][t] += 1

    if (s[i] == '0') :
        c += 1
    else :
        pre[i] = c
        c = 0



if (k == 0 or ch[n][1] - ch[0][1] < k) :
    print(1)
    exit(0)

c = 0
for i in range (n,0,-1) :
    if (s[i] == '0') :
        c += 1
    else :
        suf[i] = c
        c = 0

ans = 0

ton = 0
d = {}
d1 = {}

for i in range (n+1) :
    if (s[i] == '1') :
        d[i] = ton
        d1[ton] = i+1
        ton += 1

for i in range (1,n+1) :
    if (s[i] == '0') :
        continue

    j = i
    c = 0

    temp = d[i]

    if d1.get(temp + k - 1) is not None :
        j = d1[temp + k - 1]
    else :
        break

    #print(i,j,'a')

    z = pre[i] + suf[j-1] + ch[j-1][0] - ch[i-1][0]

    ans += (fact[z + k]*inv[k] * inv[z])%mod1
    ans %= mod1

ans1 = 0

for i in range (1,n+1) :
    if (s[i] == '0') :
        continue

    j = i
    c = 0

    temp = d[i]

    if (d1.get(temp + k) is not None) :
        j = d1[temp + k]
    else :
        break

    #print(i,j,'b')

    z = ch[j-1][0] - ch[i-1][0]

    ans1 += (fact[z + k -1]*inv[k-1]*inv[z])%mod1
    ans1 %= mod1

ans = (ans + mod1 - ans1)%mod1
print(ans)
