Chef has a circular sequence $A$ of $N$ non-negative integers $A_1, A_2, \ldots, A_N$ where $A_i$ and $A_{i+1}$ are considered adjacent, and elements $A_1$ and $A_N$ are considered adjacent.
An operation on position $p$ in array $A$ is defined as replacing $A_p$ by the bitwise OR of elements adjacent to $A_p$. Formally, an operation is defined as:
- If $p = 1$, replace $A_1$ with $A_N | A_{2}$
- If $1 < p < N$, replace $A_p$ with $A_{p-1} | A_{p+1}$
- If $p = N$, replace $A_N$ with $A_{N-1} | A_1$
Here, '|' denotes the bitwise OR operation.
Now, Chef must apply operations at each position exactly once, but he may apply the operations in any order.
Being a friend of Chef, you are required to find a sequence of operations, such that after applying all the $N$ operations, the bitwise OR of the resulting array is $K$, or determine that no such sequence of operations exist.

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $K$ denoting the number of elements, and the required bitwise OR after operations.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output:-----
For each test case, if no valid sequence of operations exist, print -1.
Otherwise, print $N$ space-separated integers in which $i$-th integer denote the position chosen in the $i$-th operation. If there are multiple valid sequences of operations, you may print any valid sequence.

-----Constraints-----
- $1 \le T \le 10^5$
- $3 \le N \le 2*10^5$
- $0 \le A_i, K \le 10^9$
- It's guaranteed that the total length of the arrays in one test file doesn't exceed $10^6$

-----Sample Input:-----
5
3 6
2 1 6
3 6
2 1 5
3 7
2 4 6
3 7
1 2 4
3 7
1 2 6

-----Sample Output:-----
2 1 3
-1
-1
-1
2 3 1

-----Explanation:-----
In the first test case, initially, the sequence is {2, 1, 6}. 
- Chef applies the operation on the $2^{nd}$ index, so the sequence converts to {2, 6, 6}.
- Next, Chef applies the operation on the $1^{st}$ index, so the sequence converts to {6, 6, 6}.
- Next, Chef applies the operation on the $3^{rd}$ index, and this time sequence does not change.
The final sequence is {6, 6, 6}, and bitwise OR of this sequence is $6$ that is equal to given $K$.

Difficulty: interview

Starter code:

Solutions:
t=int(input())
def check():
    pref = [0]*n
    pref[0]=a[0]
    suff = [0]*n
    suff[-1]=a[-1]
    for i in range (1,n):
        pref[i] = pref[i-1]|a[i]
        suff[n-i-1] = suff[n-i]|a[n-i-1]
    if suff[1]==k:
        return 0
    elif pref[n-2]==k:
        return n-1
    else:
        for i in range (1,n-1):
            if pref[i-1]|suff[i+1] == k:
                return i
        return -1
while(t):
    t-=1
    n,k=[int(i) for i in input().split()]
    a=[int(i) for i in input().split()]
    ans = []
    arr = [0]*n
    for i in range (n):
        if k|a[i] != k:
            a[i] = a[i-1]|a[(i+1)%(n)]
            ans.append(i+1)
            arr[i]=1

    x = 0
    count = 0
    for i in range (n):
        x|=a[i]
        
    if x!= k:
        print(-1)
    else:
        y = check()
        if y == -1:
            print(-1)
        else:
            for i in range (y,n+y):
                if arr[i%n]==0:
                    arr[i%n]==1
                    ans.append((i%n)+1)
            print(*ans)

# cook your dish here
tests = int(input())
for _ in range(tests):
   n, k = [int(j) for j in input().split()]
   nums = [int(j) for j in input().split()]
   check = [(j - (j & k)) != 0 for j in nums]
   impossible = check[0] and check[-1]
   for i in range(n-1):
      impossible = impossible or (check[i] and check[i+1])
   if impossible:
      print(-1)
   elif sum(check) != 0:
      start = -1
      for i in range(-1,n-1):
         if check[i]:
            nums[i] = nums[i-1] | nums[i+1]
            if start == -1:
               start = i+1
      for i in range(start,start+n):
         if not check[i%n]:
            nums[i%n] = nums[(i-1)%n] | nums[(i+1)%n]
      answer = 0
      for i in range(n):
         answer = answer | nums[i]
      if answer == k:
         for i in range(n):
            if check[i]:
               print(i+1, end = " ")
         for i in range(start,start+n):
            if not check[i%n]:
               print(i%n+1, end = " ")
         print("")
      else:
         print(-1)
   else:
      for i in range(-1,n-1):
         if nums[i] == nums[i] & (nums[i-1] | nums[i+1]):
            for j in range(i,i+n):
               nums[j%n] = nums[(j-1)%n] | nums[(j+1)%n]
            answer = 0
            for j in range(n):
               answer = answer | nums[j]
            if answer == k:
               for j in range(i,i+n):
                  print((j+n)%n+1,end = " ")
               print("")
            else:
               print(-1)
            impossible = True
            break
      if not impossible:
         for i in range(n):
            ss = list(nums)
            for j in range(i,i+n):
               ss[j%n] = ss[(j+1)%n] | ss[(j-1)%n]
            answer = 0
            for j in range(n):
               answer = answer | ss[j]
            if answer == k:
               for j in range(i,i+n):
                  print((j%n)+1,end=" ")
               print("")
               impossible = True
               break
      if not impossible:
         print(-1)
      

t=int(input())
def check():
    pref = [0]*n
    pref[0]=a[0]
    suff = [0]*n
    suff[-1]=a[-1]
    for i in range (1,n):
        pref[i] = pref[i-1]|a[i]
        suff[n-i-1] = suff[n-i]|a[n-i-1]
    if suff[1]==k:
        return 0
    elif pref[n-2]==k:
        return n-1
    else:
        for i in range (1,n-1):
            if pref[i-1]|suff[i+1] == k:
                return i
        return -1
while(t):
    t-=1
    n,k=[int(i) for i in input().split()]
    a=[int(i) for i in input().split()]
    ans = []
    arr = [0]*n
    for i in range (n):
        if k|a[i] != k:
            a[i] = a[i-1]|a[(i+1)%(n)]
            ans.append(i+1)
            arr[i]=1

    x = 0
    count = 0
    for i in range (n):
        x|=a[i]
        
    if x!= k:
        print(-1)
    else:
        y = check()
        if y == -1:
            print(-1)
        else:
            for i in range (y,n+y):
                if arr[i%n]==0:
                    arr[i%n]==1
                    ans.append((i%n)+1)
            print(*ans)


# cook your dish here
def check():
    pref = [0]*n;pref[0]=a[0];suff = [0]*n;suff[-1]=a[-1]
    for i in range (1,n):pref[i] = pref[i-1]|a[i];suff[n-i-1] = suff[n-i]|a[n-i-1]
    if suff[1]==k:return 0
    elif pref[n-2]==k:return n-1
    else:
        for i in range (1,n-1):
            if pref[i-1]|suff[i+1] == k:return i
        return -1
for z in range(int(input())):
    n,k=[int(i) for i in input().split()];a=[int(i) for i in input().split()];ans,arr = [],[0]*n
    for i in range (n):
        if k|a[i] != k:a[i] = a[i-1]|a[(i+1)%(n)];ans.append(i+1);arr[i]=1
    x = 0;count = 0
    for i in range (n):x|=a[i]      
    if x!= k:print(-1)
    else:
        y = check()
        if y == -1:print(-1)
        else:
            for i in range (y,n+y):
                if arr[i%n]==0:arr[i%n]==1;ans.append((i%n)+1)
            print(*ans)

# cook your dish here
def check():
    pref = [0]*n;pref[0]=a[0];suff = [0]*n;suff[-1]=a[-1]
    for i in range (1,n):pref[i] = pref[i-1]|a[i];suff[n-i-1] = suff[n-i]|a[n-i-1]
    if suff[1]==k:return 0
    elif pref[n-2]==k:return n-1
    else:
        for i in range (1,n-1):
            if pref[i-1]|suff[i+1] == k:return i
        return -1
for z in range(int(input())):
    n,k=[int(i) for i in input().split()];a=[int(i) for i in input().split()];ans,arr = [],[0]*n
    for i in range (n):
        if k|a[i] != k:a[i] = a[i-1]|a[(i+1)%(n)];ans.append(i+1);arr[i]=1
    x = 0;count = 0
    for i in range (n):x|=a[i]      
    if x!= k:print(-1)
    else:
        y = check()
        if y == -1:print(-1)
        else:
            for i in range (y,n+y):
                if arr[i%n]==0:arr[i%n]==1;ans.append((i%n)+1)
            print(*ans)

def check():
    pref = [0]*n;pref[0]=a[0];suff = [0]*n;suff[-1]=a[-1]
    for i in range (1,n):pref[i] = pref[i-1]|a[i];suff[n-i-1] = suff[n-i]|a[n-i-1]
    if suff[1]==k:return 0
    elif pref[n-2]==k:return n-1
    else:
        for i in range (1,n-1):
            if pref[i-1]|suff[i+1] == k:return i
        return -1
for z in range(int(input())):
    n,k=[int(i) for i in input().split()];a=[int(i) for i in input().split()];ans,arr = [],[0]*n
    for i in range (n):
        if k|a[i] != k:a[i] = a[i-1]|a[(i+1)%(n)];ans.append(i+1);arr[i]=1
    x = 0;count = 0
    for i in range (n):x|=a[i]      
    if x!= k:print(-1)
    else:
        y = check()
        if y == -1:print(-1)
        else:
            for i in range (y,n+y):
                if arr[i%n]==0:arr[i%n]==1;ans.append((i%n)+1)
            print(*ans)

t=int(input())
def check():
    pref = [0]*n
    pref[0]=a[0]
    suff = [0]*n
    suff[-1]=a[-1]
    for i in range (1,n):
        pref[i] = pref[i-1]|a[i]
        suff[n-i-1] = suff[n-i]|a[n-i-1]
    if suff[1]==k:
        return 0
    elif pref[n-2]==k:
        return n-1
    else:
        for i in range (1,n-1):
            if pref[i-1]|suff[i+1] == k:
                return i
        return -1
while(t):
    t-=1
    n,k=[int(i) for i in input().split()]
    a=[int(i) for i in input().split()]
    ans = []
    arr = [0]*n
    for i in range (n):
        if k|a[i] != k:
            a[i] = a[i-1]|a[(i+1)%(n)]
            ans.append(i+1)
            arr[i]=1

    x = 0
    count = 0
    for i in range (n):
        x|=a[i]
        
    if x!= k:
        print(-1)
    else:
        y = check()
        if y == -1:
            print(-1)
        else:
            for i in range (y,n+y):
                if arr[i%n]==0:
                    arr[i%n]==1
                    ans.append((i%n)+1)
            print(*ans)


t=int(input())
def check():
    pref = [0]*n
    pref[0]=a[0]
    suff = [0]*n
    suff[-1]=a[-1]
    for i in range (1,n):
        pref[i] = pref[i-1]|a[i]
        suff[n-i-1] = suff[n-i]|a[n-i-1]
    if suff[1]==k:
        return 0
    elif pref[n-2]==k:
        return n-1
    else:
        for i in range (1,n-1):
            if pref[i-1]|suff[i+1] == k:
                return i
        return -1
while(t):
    t-=1
    n,k=[int(i) for i in input().split()]
    a=[int(i) for i in input().split()]
    ans = []
    arr = [0]*n
    for i in range (n):
        if k|a[i] != k:
            a[i] = a[i-1]|a[(i+1)%(n)]
            ans.append(i+1)
            arr[i]=1

    x = 0
    count = 0
    for i in range (n):
        x|=a[i]
        
    if x!= k:
        print(-1)
    else:
        y = check()
        if y == -1:
            print(-1)
        else:
            for i in range (y,n+y):
                if arr[i%n]==0:
                    arr[i%n]==1
                    ans.append((i%n)+1)
            print(*ans)