human
Give me a Python code to find the minimum number of operations required to make all the characters equal to c and the x-s that he should use in his operations given the following:
Theofanis has a string s_1 s_2 ... s_n and a character c. He wants to make all characters of the string equal to c using the minimum number of operations.

In one operation he can choose a number x (1 ≤ x ≤ n) and for every position i, where i is not divisible by x, replace s_i with c. 

Find the minimum number of operations required to make all the characters equal to c and the x-s that he should use in his operations.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains the integer n (3 ≤ n ≤ 3 ⋅ 10^5) and a lowercase Latin letter c — the length of the string s and the character the resulting string should consist of.

The second line of each test case contains a string s of lowercase Latin letters — the initial string.

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case, firstly print one integer m — the minimum number of operations required to make all the characters equal to c.

Next, print m integers x_1, x_2, ..., x_m (1 ≤ x_j ≤ n) — the x-s that should be used in the order they are given.

It can be proved that under given constraints, an answer always exists. If there are multiple answers, print any.

Example

Input

3
4 a
aaaa
4 a
baaa
4 b
bzyx

Output

0
1
2
2 
2 3

Note

Let's describe what happens in the third test case: 

  1. x_1 = 2: we choose all positions that are not divisible by 2 and replace them, i. e. bzyx → bzbx.

  2. x_2 = 3: we choose all positions that are not divisible by 3 and replace them, i. e. bzbx → bbbb. 
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to find the minimum number of operations required to make all the characters equal to c and the x-s that he should use in his operations.

#Codeforces handle - "@titanalpha"
#Email id - shubhamnokiafan@gmail.com

from collections import Counter, deque
import math
from random import randint
from bisect import bisect
import sys
import re
import copy

MOD = 1000000007
MAX = sys.maxsize
MIN = -sys.maxsize

class get:
    def int():
        return list(map(int,input().split()))
    def str():
        return input().split()
    def float():
        return list(map(float,input().split()))
    def map():
        return map(int,input().split())

def sqrt(x):
    return int(math.sqrt(x))+1

def gcd(*args):
    result = args[0]
    for item in args:
        result = math.gcd(result,item)
    return result

def LCM(a,b):
    return (a*b)//(math.gcd(a,b))

def value(n):
    #basically returns the smallest positive integer which can't divide n
    if n%2 == 1:
        return 2
    else:
        for i in range(3,n,2):
            if n%i != 0:
                return i

def solve():
    n,c = input().split()
    n = int(n)
    s = input()
    if n == s.count(c):
        print(0)
        return
    k = n
    try:
        k = s[::-1].index(c)
        k = n-k
    except:
        pass
    temp = True
    #print(k)
    for i in range(n):
        if (i+1)%k == 0 and s[i] != c:
            print(2)
            print(n,n-1)
            temp = False
            break
    if temp == True:
        print(1)
        print(k)
            
    

    
    
for _ in range(int(input())):
    solve()