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
The first line contains one integer $T thin (1 <= T <= 10^5)$ denoting the number of test cases.
Each of the following $T$ lines contains two integers $X, Y thin (0 <= X, Y <= 10^9)$ indicating a test case.
For each test case, print one line containing one integer, the answer to the test case.
For the first test case:
So the answer is $1 times 2 + 2 times 6 = 14$.
## Input
The first line contains one integer $T thin (1 <= T <= 10^5)$ denoting the number of test cases.Each of the following $T$ lines contains two integers $X, Y thin (0 <= X, Y <= 10^9)$ indicating a test case.
## Output
For each test case, print one line containing one integer, the answer to the test case.
[samples]
## Note
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 $1 times 2 + 2 times 6 = 14$.
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $, let $ X_k, Y_k \in \mathbb{Z}_{\geq 0} $ be given integers.
**Constraints**
1. $ 1 \leq T \leq 10^5 $
2. $ 0 \leq X_k, Y_k \leq 10^9 $ for all $ k \in \{1, \dots, T\} $
**Objective**
For each test case $ k $, compute:
$$
S_k = \left( \sum_{i=0}^{X_k} \sum_{j=[i=0]}^{Y_k} \mathbf{1}_{i \& j = 0} \cdot \left\lfloor \log_2(i + j) + 1 \right\rfloor \right) \mod (10^9 + 7)
$$
where $ [i=0] $ is the Iverson bracket: $ [i=0] = 1 $ if $ i = 0 $, else $ 0 $, and $ \mathbf{1}_{i \& j = 0} $ is the indicator that the bitwise AND of $ i $ and $ j $ is zero.