human
PYTHON3 solution for "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.":



Can you provide a Python program to print one integer — the number of different strings which can be obtained from s by performing the described operation at most once?
assistant
#Here is Python program to print one integer — the number of different strings which can be obtained from s by performing the described operation at most once.
 from sys import stdin
from itertools import accumulate
input=stdin.readline
rn=lambda:int(input())
rns=lambda:map(int,input().split())
rl=lambda:list(map(int,input().split()))
rs=lambda:input().strip()
YN=lambda x:print('YES') if x else print('NO')
ceil_div=lambda a,b:-(-a//b)
mod=998244353

def make_nCr_mod(max_n=2*10**5):
    max_n = min(max_n, mod - 1)

    fact, inv_fact = [0] * (max_n + 1), [0] * (max_n + 1)
    fact[0] = 1
    for i in range(max_n):
        fact[i + 1] = fact[i] * (i + 1) % mod

    inv_fact[-1] = pow(fact[-1], mod - 2, mod)
    for i in reversed(range(max_n)):
        inv_fact[i] = inv_fact[i + 1] * (i + 1) % mod

    def nCr_mod(n, r):
        res = 1
        while n or r:
            a, b = n % mod, r % mod
            if a < b:
                return 0
            res = res * fact[a] % mod * inv_fact[b] % mod * inv_fact[a - b] % mod
            n //= mod
            r //= mod
        return res

    return nCr_mod


n,k=rns()
a=list(map(int,rs()))
acc=list(accumulate(a))
# print(acc)
def solve():
    j=0
    ans=1
    choose=make_nCr_mod()
    first=True
    for i in range(n):
        # j+=1
        if j==n:
            break
        while j<n and acc[j]-acc[i]+a[i]<=k:
            if acc[j]-acc[i]+a[i]==k:
                add=0
                if not first:
                    if a[j]==0:
                        add=choose(j-i,k-1)
                    elif j-i+1>k:
                        add=choose(j-i,k)
                else:
                    if a[j]==0:
                        add=choose(j-i+1,k-1)-1
                    elif j-i+1>k:
                        add=choose(j-i+1,k)-1
                    first=False
                ans+=add
                ans%=mod
                # print(i,j,add)
            j+=1
    return ans
print(solve())