description: 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.
solution: import java.util.*;
  import java.io.*;
  
  public class Main {
      public static void main(String args[]) {new Main().run();}
  
      FastReader in = new FastReader();
      PrintWriter out = new PrintWriter(System.out);
      void run() {
          work();
          out.flush();
      }
      long mod=998244353;
      long gcd(long a,long b) {
          return a==0?b:gcd(b%a,a);
      }
      long inf=Long.MAX_VALUE/3;
      int n,k;
      char[] chs;
      long[] rec,inv;
      void work() {
          n=ni();k=ni();
          chs=ns().toCharArray();
          rec=new long[10001];
          inv=new long[10001];
          rec[0]=1;
          inv[0]=1;
          for(int i=1;i<=10000;i++){
              rec[i]=rec[i-1]*i%mod;
          }
          inv[10000]=pow(rec[10000],mod-2);
          for(int i=9999;i>=0;i--){
              inv[i]=(i+1)*inv[i+1]%mod;
          }
          long ret=0;
          List<Integer> list=new ArrayList<>();
          for(int i=0;i<n;i++){
              if(chs[i]=='1'){
                  list.add(i);
              }
          }
          list.add(n);
          int size=list.size();
          if(k>size-1||k==0){
              out.println(1);
              return;
          }
          for(int i=0;i+k<size;i++){
              int j=i+k;
              int s=i==0?0:(list.get(i-1)+1);
              int e=list.get(j)-1;
              int m=list.get(i);
              ret+=C(j-i,e-s+1);
              if(j!=size-1)ret-=C(j-i-1,e-m);
              ret=(ret%mod+mod)%mod;
          }
          out.println(ret);
      }
  
      long C(int a,int b){
          return rec[b]*inv[a]%mod*inv[b-a]%mod;
      }
  
      private long pow(long a, long b) {
          long ret=1;
          while(b>0){
              if(b%2==1){
                  ret=ret*a%mod;
              }
              b/=2;
              a=a*a%mod;
          }
          return ret;
      }
  
  
      @SuppressWarnings("unused")
      private ArrayList<Integer>[] ng(int n, int m) {
          ArrayList<Integer>[] graph=(ArrayList<Integer>[])new ArrayList[n];
          for(int i=0;i<n;i++) {
              graph[i]=new ArrayList<>();
          }
          for(int i=1;i<=m;i++) {
              int s=in.nextInt()-1,e=in.nextInt()-1;
              graph[s].add(e);
              graph[e].add(s);
          }
          return graph;
      }
  
      private ArrayList<long[]>[] ngw(int n, int m) {
          ArrayList<long[]>[] graph=(ArrayList<long[]>[])new ArrayList[n];
          for(int i=0;i<n;i++) {
              graph[i]=new ArrayList<>();
          }
          for(int i=1;i<=m;i++) {
              long s=in.nextLong()-1,e=in.nextLong()-1,w=in.nextLong();
              graph[(int)s].add(new long[] {e,w});
              graph[(int)e].add(new long[] {s,w});
          }
          return graph;
      }
  
      private ArrayList<int[]>[] ngwi(int n, int m) {
          ArrayList<int[]>[] graph=(ArrayList<int[]>[])new ArrayList[n];
          for(int i=0;i<n;i++) {
              graph[i]=new ArrayList<>();
          }
          for(int i=1;i<=m;i++) {
              int s=ni()-1,e=ni()-1,w=ni();
              graph[s].add(new int[] {e,w});
              graph[e].add(new int[] {s,w});
          }
          return graph;
      }
  
      private int ni() {
          return in.nextInt();
      }
  
      private long nl() {
          return in.nextLong();
      }
      private double nd() {
          return in.nextDouble();
      }
      private String ns() {
          return in.next();
      }
  
      private long[] na(int n) {
          long[] A=new long[n];
          for(int i=0;i<n;i++) {
              A[i]=in.nextLong();
          }
          return A;
      }
  
      private int[] nia(int n) {
          int[] A=new int[n];
          for(int i=0;i<n;i++) {
              A[i]=in.nextInt();
          }
          return A;
      }
  }
  
  class FastReader
  {
      BufferedReader br;
      StringTokenizer st;
      InputStreamReader input;//no buffer
      public FastReader()
      {
          br=new BufferedReader(new InputStreamReader(System.in));
      }
  
      public FastReader(boolean isBuffer)
      {
          if(!isBuffer){
              input=new InputStreamReader(System.in);
          }else{
              br=new BufferedReader(new InputStreamReader(System.in));
          }
      }
  
      public boolean hasNext(){
          try{
              String s=br.readLine();
              if(s==null){
                  return  false;
              }
              st=new StringTokenizer(s);
          }catch(IOException e){
              e.printStackTrace();
          }
          return true;
      }
  
      public String next()
      {
          if(input!=null){
              try {
                  StringBuilder sb=new StringBuilder();
                  int ch=input.read();
                  while(ch=='\n'||ch=='\r'||ch==32){
                      ch=input.read();
                  }
                  while(ch!='\n'&&ch!='\r'&&ch!=32){
                      sb.append((char)ch);
                      ch=input.read();
                  }
                  return sb.toString();
              }catch (Exception e){
                  e.printStackTrace();
              }
          }
          while(st==null || !st.hasMoreElements())//回车，空行情况
          {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
  
      public int nextInt()
      {
          return (int)nextLong();
      }
  
      public long nextLong() {
          try {
              if(input!=null){
                  long ret=0;
                  int b=input.read();
                  while(b<'0'||b>'9'){
                      b=input.read();
                  }
                  while(b>='0'&&b<='9'){
                      ret=ret*10+(b-'0');
                      b=input.read();
                  }
                  return ret;
              }
          }catch (Exception e){
              e.printStackTrace();
          }
          return Long.parseLong(next());
      }
  
      public double nextDouble()
      {
          return Double.parseDouble(next());
      }
  }