CF1614C.Divan and bitwise operations

Once Divan analyzed a sequence $a_1, a_2, \ldots, a_n$ consisting of $n$ non-negative integers as follows. He considered each non-empty subsequence of the sequence $a$ , computed the bitwise XOR of its elements and added up all the XORs, obtaining the coziness of the sequence $a$ .

A sequence $c$ is a subsequence of a sequence $d$ if $c$ can be obtained from $d$ by deletion of several (possibly, zero or all) elements. For example, $[1, \, 2, \, 3, \, 4]$ , $[2, \, 4]$ , and $[2]$ are subsequences of $[1, \, 2, \, 3, \, 4]$ , but $[4, \, 3]$ and $[0]$ are not.

Divan was very proud of his analysis, but now he lost the sequence $a$ , and also the coziness value! However, Divan remembers the value of bitwise OR on $m$ contiguous subsegments of the sequence $a$ . It turns out that each element of the original sequence is contained in at least one of these $m$ segments.

Divan asks you to help find the coziness of the sequence $a$ using the information he remembers. If several coziness values are possible, print any.

As the result can be very large, print the value modulo $10^9 + 7$ .

The first line contains one integer number $t$ ( $1 \le t \le 10^3$ ) — the number of test cases.

The first line of each test case contains two integer numbers $n$ and $m$ ( $1 \le n, m \le 2 \cdot 10^5$ ) — the length of the sequence and the number of contiguous segments whose bitwise OR values Divan remembers, respectively.

The following $m$ lines describe the segments, one per line.

Each segment is described with three integers $l$ , $r$ , and $x$ ( $1 \le l \le r \le n$ , $0 \le x \le 2^{30} - 1$ ) — the first and last elements of the segment and the bitwise OR of $a_l, a_{l + 1}, \ldots, a_r$ , respectively.

It is guaranteed that each element of the sequence is contained in at least one of the segments. It is guaranteed that there exists a sequence that satisfies all constraints.

It is guaranteed that the sum of $n$ and the sum of $m$ over all test cases do not exceed $2 \cdot 10^5$ .

For each test case print the coziness any suitable sequence $a$ modulo $10^9 + 7$ .

In first example, one of the sequences that fits the constraints is $[0, 2]$ . Consider all its non-empty subsequences:

• $[0]$ : the bitwise XOR of this subsequence is $0$ ;
• $[2]$ : the bitwise XOR of this subsequence is $2$ ;
• $[0, 2]$ : the bitwise XOR of this subsequence is $2$ .

The sum of all results is $4$ , so it is the answer.

In second example, one of the sequences that fits the constraints is $[0, \, 5, \, 5]$ .

In third example, one of the sequences that fits the constraints is $[5, \, 6, \, 7, \, 0, \, 2]$ .