Moamen and XOR solution codeforces

For Solution

Click Here!

Moamen and Ezzat are playing a game. They create an array $a$ of $n$ non-negative integers where every element is less than $2^{k}$ .

Moamen wins if $a_{1} & a_{2} & a_{3} & \dots & a_{n} \geq a_{1} \oplus a_{2} \oplus a_{3} \oplus \dots \oplus a_{n}$ .

Here $&$ denotes the bitwise AND operation, and $\oplus$ denotes the bitwise XOR operation.

Please calculate the number of winning for Moamen arrays $a$ .

As the result may be very large, print the value modulo $1 000 000 007$ ( $10^{9} + 7$ ).

Input Moamen and XOR solution codeforces

The first line contains a single integer $t$ ( $1 \leq t \leq 5$ )— the number of test cases.

Each test case consists of one line containing two integers $n$ and $k$ ( $1 \leq n \leq 2 \cdot 10^{5}$ , $0 \leq k \leq 2 \cdot 10^{5}$ ).

Output Moamen and XOR solution codeforces

For each test case, print a single value — the number of different arrays that Moamen wins with.

Print the result modulo $1 000 000 007$ ( $10^{9} + 7$ ).

Example Moamen and XOR solution codeforces

input

Copy

output Moamen and XOR solution codeforces

Copy

5
2
1

Note

In the first example, $n = 3$ , $k = 1$ . As a result, all the possible arrays are $[0, 0, 0]$ , $[0, 0, 1]$ , $[0, 1, 0]$ , $[1, 0, 0]$ , $[1, 1, 0]$ , $[0, 1, 1]$ , $[1, 0, 1]$ , and $[1, 1, 1]$ .

Moamen wins in only $5$ of them: $[0, 0, 0]$ , $[1, 1, 0]$ , $[0, 1, 1]$ , $[1, 0, 1]$ , and $[1, 1, 1]$ .

For Solution

Click Here!

Ezzat and Two Subsequences standard input/output 1 s, 256 MB
B	Moamen and k-subarrays standard input/output 2 s, 256 MB
C	Moamen and XOR standard input/output 2 s, 256 MB
D	Ezzat and Grid standard input/output 2.5 s, 256 MB
E	Assiut Chess standard input/output 1 s, 256 MB

Moamen and XOR solution codeforces

For Solution

Click Here!

For Solution

Click Here!

Leave a Comment Cancel Reply