Alice has $$$a$$$ coins. She can open a bank deposit called "Profitable", but the minimum amount required to open this deposit is $$$b$$$ coins.

There is also a deposit called "Unprofitable", which can be opened with any amount of coins. Alice noticed that if she opens the "Unprofitable" deposit with $$$x$$$ coins, the minimum amount required to open the "Profitable" deposit decreases by $$$2x$$$ coins. However, these coins cannot later be deposited into the "Profitable" deposit.

Help Alice determine the maximum number of coins she can deposit into the "Profitable" deposit if she first deposits some amount of coins (possibly $$$0$$$) into the "Unprofitable" deposit. If Alice can never open the "Profitable" deposit, output $$$0$$$.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

A single line of each test case contains two integers $$$a$$$ and $$$b$$$ ($$$1 \le a, b \le 10^9$$$) — the number of coins Alice has and the initial minimum amount required to open the "Profitable" deposit.

Output

For each test case, output a single integer — the maximum number of coins that Alice can deposit into the "Profitable" deposit. If Alice can never open the "Profitable" deposit, output $$$0$$$.

Note

In the first test case, $$$a \ge b$$$, so Alice can immediately open the "Profitable" deposit with all $$$10$$$ coins.

In the second test case, Alice can open the "Unprofitable" deposit with $$$2$$$ coins. Then she will have $$$5$$$ coins left, but the minimum amount required to open the "Profitable" deposit will decrease by $$$4$$$ coins, making it equal to $$$5$$$ coins. Thus, Alice will be able to open the "Profitable" deposit with $$$5$$$ coins.

In the third test case, Alice will not be able to open the "Profitable" deposit.

Profitable Interest Rate

Examples