human
Can you provide 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.

try:
        import sys
        from functools import lru_cache, cmp_to_key
        from heapq import merge, heapify, heappop, heappush
        # from math import *
        from collections import defaultdict as dd, deque, Counter as C
        from itertools import combinations as comb, permutations as perm
        from bisect import bisect_left as bl, bisect_right as br, bisect, insort
        from time import perf_counter
        from fractions import Fraction
        import copy
        from copy import deepcopy
        import time
        starttime = time.time()
        mod = int(pow(10, 9) + 7)
        mod2 = 998244353

        def data(): return sys.stdin.readline().strip()
        def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
        def L(): return list(sp())
        def sl(): return list(ssp())
        def sp(): return map(int, data().split())
        def ssp(): return map(str, data().split())
        def l1d(n, val=0): return [val for i in range(n)]
        def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
        def A2(n,m): return [[0]*m for i in range(n)]
        def A(n):return [0]*n
        # sys.setrecursionlimit(int(pow(10,6)))
        # from sys import stdin
        # input = stdin.buffer.readline
        # I = lambda : list(map(int,input().split()))
        # import sys
        # input=sys.stdin.readline
        

        sys.stdin = open("input.txt", "r")
        sys.stdout = open("output.txt", "w")
except:
        pass


for _ in range(L()[0]):
        X = input().split()
        n = int(X[0])
        c = X[1]

        s = input()
        i = n-1
        if c not in s:
                print(2)
                print(n-1,n)
        elif s.count(c)==n:
                print(0)
        else:
                while(s[i]!=c):
                        i-=1
                i+=1
                if i*2<=n:
                        print(2)
                        print(n-1,n)
                else:
                        print(1)
                        print(i)