Chef has an array consisting of N + K - 1 integers. The array contains only the first N positive odd numbers. Each number appears exactly once, except for one number which appears exactly K times. The sum of integers in Chef's array is equal to S.

For example, for N = 3, K = 2, the possible arrays could be [1, 1, 3, 5], [3, 1, 3, 5], [5, 3, 5, 1]. For N = 1, K = 3, there is only one possible array: [1, 1, 1].

Chef gives you three integers N, K and S and asks you to find the only element which appears K times in his array.

It is guaranteed that for the given input, there exists a valid array consisting of N + K -1 elements with a sum exactly equal to S.

------ Input Format ------

• The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• The first and only line of each test case contains three space-separated integers N, K, S.

------ Output Format ------

For each test case, print a single line containing the integer which appeared K times in Chef's array.

------ Constraints ------

$1 ≤ T ≤ 1000$
$1 ≤ N ≤ 10^{4}$
$1 ≤ S ≤ 10^{9}$
$2 ≤ K ≤ 10^{4}$

----- Sample Input 1 ------
3
3 2 14
5 4 28
2 3 10

----- Sample Output 1 ------
5
1
3

----- explanation 1 ------
Test case $1$: Chef's array could be $[5, 3, 5, 1]$.

Test case $3$: Chef's array could be $[3, 1, 3, 3]$.

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