codeforces_738D

D. Sea Battle

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Galya is playing one-dimensional Sea Battle on a 1 × n grid. In this game a ships are placed on the grid. Each of the ships consists of b consecutive cells. No cell can be part of two ships, however, the ships can touch each other.

Galya doesn't know the ships location. She can shoot to some cells and after each shot she is told if that cell was a part of some ship (this case is called "hit") or not (this case is called "miss").

Galya has already made k shots, all of them were misses.

Your task is to calculate the minimum number of cells such that if Galya shoot at all of them, she would hit at least one ship.

It is guaranteed that there is at least one valid ships placement.

Input

The first line contains four positive integers n, a, b, k (1 ≤ n ≤ 2·105, 1 ≤ a, b ≤ n, 0 ≤ k ≤ n - 1) — the length of the grid, the number of ships on the grid, the length of each ship and the number of shots Galya has already made.

The second line contains a string of length n, consisting of zeros and ones. If the i-th character is one, Galya has already made a shot to this cell. Otherwise, she hasn't. It is guaranteed that there are exactly k ones in this string.

Output

In the first line print the minimum number of cells such that if Galya shoot at all of them, she would hit at least one ship.

In the second line print the cells Galya should shoot at.

Each cell should be printed exactly once. You can print the cells in arbitrary order. The cells are numbered from 1 ton, starting from the left.

If there are multiple answers, you can print any of them.

Examples

input

5 1 2 1
00100

output

2
4 2

input

13 3 2 3
1000000010001

output

2
7 11

Note

There is one ship in the first sample. It can be either to the left or to the right from the shot Galya has already made (the "1" character). So, it is necessary to make two shots: one at the left part, and one at the right part.

 题意：1*n的矩阵上，a条船，每条都是b的长度，已经开了k炮，每个格子只能被一条船占据。问最少再开多少炮能至少击中一条船，输出这几炮的位置。

比赛是以为搞不出来，结果给搞出来了，开心！！！

思路：抽象一下，也就是说，在序列中某些位置加上1后，序列中能放下的长度b的0序列的个数<=a-1。

#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
#define N 200005

struct Seg
{
    int l,r,dis;
} seg[N];
bool cmp(Seg a,Seg b)
{
    return a.dis>b.dis;
}

int main()
{
    int n,a,b,k;
    char str[N];
    scanf("%d%d%d%d",&n,&a,&b,&k);
    scanf("%s",str);
    int st=0,en=0,p=0,cnt=0;
    while(p<n)
    {
        if(str[p]=='1')
        {
            en=p-1;
            Seg se;
            se.l=st;
            se.r=en;
            se.dis=en-st+1;
            if(se.l<=se.r)
                seg[cnt++]=se;
            while(str[p]=='1')
                p++;
            st=en=p;
        }
        if(str[n-1]=='0'&&p==n-1)
        {
            en=n-1;
            Seg se;
            se.l=st;
            se.r=en;
            se.dis=en-st+1;
            if(se.l<=se.r)
                seg[cnt++]=se;
        }
        p++;
    }
    sort(seg,seg+cnt,cmp);
    int ans[N],cnta=0;
    int cntt=0;
    for(int i=0; i<cnt; i++)
        for(int j=seg[i].l+b-1; j<=seg[i].r; j+=b)
        {
            if(cntt>=a-1)
                ans[cnta++]=j+1;
            else
                cntt++;
        }
    printf("%d
",cnta);
    for(int i=0; i<cnta; i++)
    {
        printf("%d",ans[i]);
        if(i==cnta-1)
            printf("
");
        else
            printf(" ");
    }
    return 0;
}