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For two arrays $$$a = [a_1, a_2, \dots, a_n]$$$ and $$$b = [b_1, b_2, \dots, b_m]$$$, we define the XOR matrix $$$X$$$ of size $$$n \times m$$$, where for each pair $$$(i,j)$$$ ($$$1 \le i \le n$$$; $$$1 \le j \le m$$$) it holds that $$$X_{i,j} = a_i \oplus b_j$$$. The symbol $$$\oplus$$$ denotes the bitwise XOR operation.

You are given four integers $$$n, m, A, B$$$. Count the number of such pairs of arrays $$$(a, b)$$$ such that:

$$$a$$$ consists of $$$n$$$ integers, each of which is from $$$0$$$ to $$$A$$$;
$$$b$$$ consists of $$$m$$$ integers, each of which is from $$$0$$$ to $$$B$$$;
in the XOR matrix formed from these arrays, there are no more than two distinct values.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case consists of one line containing four integers $$$n, m, A, B$$$ ($$$2 \le n, m, A, B \le 2^{29} - 1$$$).

XOR Matrix

Examples