随机 - Problem

#4385. 随机

Statistics

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

有 $N$ 个在 $[0, 1]$ 之间随机生成的数。进行 $M$ 次操作，每次操作以 $\frac{1}{2}$ 的概率删除当前的最大值，以 $\frac{1}{2}$ 的概率删除当前的最小值。计算剩余数值之和的期望值，对 $10^9 + 7$ 取模。

输入格式

每个测试点包含多个测试用例。第一行包含测试用例的数量 $T(1 \le T \le 10000)$。接下来是各测试用例的描述。每个测试用例的第一行包含两个整数 $n, m$。 $1 \le m \le n \le 10^9$

输出格式

对于每个测试用例，输出一个整数，即问题的答案。

样例

样例输入 1

2
2 2
3 1

样例输出 1

0
1

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