题目描述

Given two non-negative integers $X$ and $Y$, determine the value of

$$\sum_{i=0}^{X}\sum_{j=[i=0]}^{Y}[i\&j=0]\lfloor\log_2(i+j)+1\rfloor $$

modulo $10^9+7$ where

• $\&$ denotes bitwise AND;
• $[A]$ equals 1 if $A$ is true, otherwise $0$;
• $\lfloor x\rfloor$ equals the maximum integer whose value is no more than $x$.

输入格式

The first line contains one integer $T\,(1\le T \le 10^5)$ denoting the number of test cases.

Each of the following $T$ lines contains two integers $X, Y\,(0\le X,Y \le 10^9)$ indicating a test case.

输出格式

For each test case, print one line containing one integer, the answer to the test case.

3
3 3
19 26
8 17

14
814
278

提示

For the first test case:

• Two $(i,j)$ pairs increase the sum by 1: $(0, 1), (1, 0)$
• Six $(i,j)$ pairs increase the sum by 2: $(0, 2), (0, 3), (1, 2), (2, 0), (2, 1), (3, 0)$

So the answer is $1\times 2 + 2\times 6 = 14$.