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 ≤ 2·10^5, 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 to n, 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.

Difficulty: interview

Starter code:

Solutions:
def sum_zeroth(arr):
    res = 0
    for elem in arr:
        res += elem[0]
    return res

n, a, b, k = list(map(int, input().split()))
data = input()
dist = []
pp = 0

last = 0
for i in range(n):
    if data[i] == '1':
        dist.append((last, i))
        pp += (i - last) // b
        last = i + 1

dist.append((last, n))
pp += (n - last) // b
pos = []
minp = pp - a + 1
fnd = False

for elem in dist:
    cur = elem[0] - 1
    while (cur + b) < elem[1]:
        cur += b
        pos.append(cur + 1)
        if len(pos) == minp:
            fnd = True
            break
    if fnd:
        break

print(minp)
print(' '.join(map(str, pos)))


n, a, b, k = map(int, input().split())
s = input()
ind = 0
ans = []
 
for i in range(k):
    l = s[ind:].find("1")
    if (l ) >= b:
        ans.append([l , ind, ind + l])
    ind += l + 1
 
if (len(s) - ind ) >= b:
    ans.append([len(s) - ind , ind, len(s)])
#print(ans)
 
aans = []
count = 0
for i in range(len(ans)):
    j = ans[i][1] - 1
    while j + b < ans[i][2]:
        j += b
        aans.append(j + 1)
       
#print(*aans)
l = len(aans) - a + 1
aans =aans[:l]
print(len(aans))
print(*aans)

n,a,b,k = map(int,input().split())
A=['1'] + list(input()) + ['1']
answer =[]
n+= 2
i = 0
while i <= n-2:
    per = 0
    for j in range(i+1, i+b+1):
        if j > n - 1:
            break
        if A[j] == '1':
            i = j
            per = 1
            break
    if per == 0:
        i = j
        answer.append(i)
lens = len(answer)
print(lens - a +1)
print(' '.join(map(str, answer[0:lens-a+1])))

n,a,b,k=[int(i) for i in input().split()]
s=input()
l=[]
i=0
j=0
while i<len(s):
	if s[i]=="1":
		j=0
	else :
		j+=1
		if(j%b)==0:
			l+=[i+1]
			j=0
	i+=1
l=l[a-1:]
print(len(l))
print(*l)




n,a,b,k=list(map(int,input().split()))
A=input()
B=A.split('1')
C=[]
l=1

for i in B:
    if len(i)>=b:
        for j in range(b-1,len(i),b):
            C.append(j+l)
    l+=len(i)+1
C=C[:len(C)-a+1]
print(len(C))
print(' '.join(list(map(str,C))))



n, s, b, k = map(int, input().split())
a = list('1' + input() + '1')
ans = []
cnt = 0
for i in range(len(a)):
    if a[i] == '0':
        cnt += 1
    else:
        cnt = 0
    if cnt == b:
        if s > 1:
            s -= 1
        else:
            ans.append(i)
        cnt = 0
print(len(ans))
for i in range(len(ans)):
    print(ans[i], end=' ')

'''input
5 4 1 0
00000
'''
from sys import stdin
import collections
import math


def get_working(string):
	aux = []
	first = None
	if string[0] == 1:
		pass
	else:
		first = -1
	for i in range(len(string)):
		if string[i] == '1':
			if first == None:
				first = i
			elif first != None:
				aux.append([first, i, (i - first - 1)])
				first = i
	if first != None:
		aux.append([first, len(string), (len(string) - first) - 1])

	return aux


# main starts
n, a, b, k = list(map(int, stdin.readline().split()))
string = list(stdin.readline().strip())

ans  = 0
working = get_working(string)
# print(working)
current = a
flag = 0
for i in working:
	if flag == 1:
		break
	start, end, gap = i
	
	j = end - 1
	if gap//b > 0:
		while j > start:
			if current == 0:
				flag = 1
				break
			if (j - start)// b > 0:
				for k in range(j, j - b, -1):
					string[k] = '2'
				j -= b	
				current -= 1
			else:
				break
ans = []
count = 0
for i in range(len(string)):
	if string[i] == '0':
		if i > 0 and string[i - 1] == '0':
			count += 1
		else:
			count = 1

		if count == b:
			string[i] = 'b'
			ans.append(i + 1)
			count = 0
		
			
for i in range(len(string)):
	if string[i] == '2':
		ans.append(i + 1)
		break
# print(string)
print(len(ans))
print(*ans)
# print(ans)
# for i in range(n):
# 	if string[i] == 'b':
# 		print(i + 1, end = ' ')


# Why do we fall ? So we can learn to pick ourselves up.


from itertools import groupby
n,a,b,k = map(int,input().split())
s = input()
sg = [list(g) for s,g in groupby(s)]
ll = 0
hits = []
for i in range(0,len(sg)):
    if sg[i][0] == '0' and len(sg[i]) >= b:
        for hit in range(b-1,len(sg[i]),b):
            hits.append(hit+ll+1)
        ll += len(sg[i])
    else:
        ll += len(sg[i])
# print(hits)
hits = hits[a-1:]
print(len(hits))
print(*hits)





"""

13 3 2 3
1000000010001


15 3 2 3
1000000000010001

"""

# Why do we fall ? So we can learn to pick ourselves up.


from itertools import groupby
n,a,b,k = map(int,input().split())
s = input()
sg = [list(g) for s,g in groupby(s)]
ll = 0
hits = []
for i in range(0,len(sg)):
    if sg[i][0] == '0' and len(sg[i]) >= b:
        for hit in range(b-1,len(sg[i]),b):
            hits.append(hit+ll+1)
        ll += len(sg[i])
    else:
        ll += len(sg[i])
# print(hits)
# We remove number of (ships-1) from the total number of hits because we are hitting at every possible location where
# where the ship can be placed and since we want to hit AT LEAST ONE SHIP, removing (ships-1) will still hit at least one ship 
hits = hits[a-1:]
print(len(hits))
print(*hits)





"""

13 3 2 3
1000000010001


15 3 2 3
1000000000010001

"""

import heapq
from itertools import groupby


def read_int():
    return int(input().strip())


def read_ints():
    return list(map(int, input().strip().split(' ')))


def ilen(ll):
    return sum(1 for _ in ll)

def solve():
    """
    13 3 2 3
    1000000010001
        3     1
    000000000
      a, b

    - how many shots do you need to reduce maximum possible number of ships in a segment?
    1 1 1 0
    0
    """
    n, a, b, k = read_ints()
    s = input().strip()
    segments = [] # (length, start)
    maximum_count = 0
    for start, vals in groupby(enumerate(s), key=lambda p: p[1]):
        val = next(vals)
        if val[1] == '0':
            segments.append((val[0], 1+ilen(vals)))
            maximum_count += segments[-1][1]//b
    shots = []
    while maximum_count >= a:
        start, length = segments.pop()
        if length//b > 0:
            shots.append(start+b-1)
            segments.append((start+b, length-b))
            maximum_count -= 1
    print(len(shots))
    print(' '.join([str(shot+1) for shot in shots]))

    
def __starting_point():
    solve()

__starting_point()

"Codeforces Round #384 (Div. 2)"
"C. Vladik and fractions"
# y=int(input())
# a=y
# b=a+1
# c=y*b
# if y==1:
#     print(-1)
# else:    
#     print(a,b,c)
"Technocup 2017 - Elimination Round 2"
"D. Sea Battle"
n,a,b,k=map(int,input().split())
s=list(input())
n=len(s)
lz=[]
zeros=[]
indexes=[]
flage=0
if s[0]=="0":
    lz.append(0)
    flage=1  
for i in range(1,n):
    if flage==1 and s[i]=="1":
        zeros.append(i-1-(lz[-1])+1)
        lz.append(i-1)
        flage=0
    elif flage==0 and s[i]=="0":
        lz.append(i)
        flage=1   

if s[-1]=="0":
    zeros.append(n-1-(lz[-1])+1)
    lz.append(n-1)
min_no_spaces=(a-1)*b
spaces_left=n-k    
l=len(lz)    
# print(lz)
# print(zeros)  
shotes=0
for i in range(len(zeros)):
    h=i*2
    if min_no_spaces!=0:
        # print(min_no_spaces)
        if min_no_spaces>=zeros[i]:
            min_no_spaces-=(int(zeros[i]/b))*b
        elif min_no_spaces<zeros[i]:
            shotes+=int((zeros[i]-min_no_spaces)/b)
            for j in range(int((zeros[i]-min_no_spaces)/b)):
                indexes.append(lz[h]+((j+1)*b))
            min_no_spaces=0    
    elif min_no_spaces==0:
        # print(min_no_spaces)
        shotes+=int(zeros[i]/b)
        for j in range(int(zeros[i]/b)):
            indexes.append(lz[h]+((j+1)*b))
print(shotes)
for i in indexes:
    print(i," ",end="",sep="")

n,a,b,k = list(map(int,input().split()))

s = input()

sm = 0
num = 0
res = []
for i in range(n):
    if s[i] == "1":
        sm = 0
    if s[i] == "0":
        sm += 1
        if sm == b:
            num += 1
            res.append(i+1)
            sm = 0
k = num - a + 1
print(k)
print(*res[:k])