Let $$$bit(x)$$$ denote the number of ones in the binary representation of a non-negative integer $$$x$$$.

A subarray of an array is called $$$k$$$-good if it consists only of numbers with no more than $$$k$$$ ones in their binary representation, i.e., a subarray $$$(l, r)$$$ of array $$$a$$$ is good if for any $$$i$$$ such that $$$l \le i \le r$$$ condition $$$bit(a_{i}) \le k$$$ is satisfied.

You are given an array $$$a$$$ of length $$$n$$$, consisting of consecutive non-negative integers starting from $$$0$$$, i.e., $$$a_{i} = i$$$ for $$$0 \le i \le n - 1$$$ (in $$$0$$$-based indexing). You need to count the number of $$$k$$$-good subarrays in this array.

As the answer can be very large, output it modulo $$$10^{9} + 7$$$.

Input

Each test consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^{4}$$$) — the number of test cases. The following lines describe the test cases.

The single line of each test case contains two integers $$$n$$$, $$$k$$$ ($$$1 \le n \le 10^{18}, 1 \le k \le 60$$$).

Output

For each test case, output a single integer — the number of $$$k$$$-good subarrays modulo $$$10^{9} + 7$$$.

Note

For the first test case $$$a = [0, 1, 2, 3, 4, 5]$$$, $$$k = 1$$$.

To find the answer, let's write all the numbers in binary representation:

$$$$$$a = [\color{green}{000}, \color{green}{001}, \color{green}{010}, \color{red}{011}, \color{green}{100}, \color{red}{101}]$$$$$$

From this, it can be seen that the numbers $$$3$$$ and $$$5$$$ have $$$2 \ge (k = 1)$$$ ones in their binary representation, so the answer should include all subarrays that do not contain either $$$3$$$ or $$$5$$$, which are the subarrays (in $$$0$$$-based indexing): ($$$0$$$, $$$0$$$), ($$$0$$$, $$$1$$$), ($$$0$$$, $$$2$$$), ($$$1$$$, $$$1$$$), ($$$1$$$, $$$2$$$), ($$$2$$$, $$$2$$$), ($$$4$$$, $$$4$$$).

Number of k-good subarrays

Examples