Make All Elements 0
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Description
You are given an array $a$ of $n$ non-negative integers and an integer $k$.
In one operation you can do:
- choose two integers $l,r(1 \le l \le r \le n)$ and a positive integer $x(1 \le x \le k)$, after that make $a_i:=a_i\&x$ for all $l \le i \le r$.
Here $\&$ denotes the bitwise AND operation.
Find the minimum number of operations to make all elements to zero.
If it's impossible to make all elements to zero, output $-1$ instead.
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10000$). The description of the test cases follows.
The first line of each testcase contains two integers $n,k$ ($1 \le n,k \le 10000$).
The second line of each testcase contains $n$ integers $a_1,a_2,\ldots, a_n$ ($0 \le s_i \le 10000$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10000$.
For each test case, print a single integer — the minimum number of operations to make all elements to zero. If it's impossible to make all elements to zero, output $-1$ instead.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10000$). The description of the test cases follows.
The first line of each testcase contains two integers $n,k$ ($1 \le n,k \le 10000$).
The second line of each testcase contains $n$ integers $a_1,a_2,\ldots, a_n$ ($0 \le s_i \le 10000$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10000$.
Output
For each test case, print a single integer — the minimum number of operations to make all elements to zero. If it's impossible to make all elements to zero, output $-1$ instead.
4
1 1
0
4 4
1 3 2 8
4 3
1 3 2 8
8 1
1 5 17 29 1000 11 45 22
0
1
2
-1