Chef and the stones

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Chef has two piles of stones with him, one has n₁ stones and the other has n₂ stones. Fired up by boredom, he invented a game with the two piles.

Before the start of the game Chef chooses an integer m.

In the j-th move:

• He chooses a number x_j such that 1 ≤ x_j ≤ m, and removes x_j stones from both the piles (this is only possible when both the piles have ≥ x_j stones).
• The number chosen must be unique over all the moves in the game. That is, for all k < j, x_j ≠ x_k.

Chef wants to make the moves in such a way that the sum of the number of stones remaining in the two piles is minimized. Please help Chef find this.

Input

• The first line of input contains an integer T denoting the number of test cases.
• Each test case consists of 1 line with three integers — n₁, n₂ and m — separated by single spaces.

Output

For each test case, output a single line containing the minimum sum of the number of stones of two piles.

Constraints

Subtask 1 : (5 pts)

• 1 ≤ T ≤ 100
• 0 ≤ m ≤ 18
• 0 ≤ n₁, n₂ ≤ 100

Subtask 2 : (25 pts)

• 1 ≤ T ≤ 1000
• 0 ≤ m ≤ 10000
• 0 ≤ n₁, n₂ ≤ 10000

Subtask 3 : (70 pts)

• 1 ≤ T ≤ 10⁵
• 0 ≤ m ≤ 10⁹
• 0 ≤ n₁, n₂ ≤ 10¹⁸

Example

Input:
3
1 1 1
1 2 1
4 5 2

Output:
0
1
3

Explanation

Example case 1. : Remove 1 stone from each of the piles. Now 0 stones are remaining, so chef cannot remove any more stones from the piles. Hence, answer is 0+0 = 0

Example case 2. : Again, remove 1 stone from both the piles to get (0,1) stones. Now chef cannot remove any more stones from pile 1, so he stops. Hence, answer is 0+1 = 1.

Example case 3. : First remove 1 stone from both the piles to get (3,4) stones. Now, remove 2 stones from both the piles so that (1,2) stones are remaining. Now chef cannot remove any more stones owing to the condition that he cannot remove the same number of stones twice. So, the answer is 1+2 = 3.