Chef is given two integers N, S.

Consider an array A of size N such that A[i]=i for every 1 ≤ i ≤ N.

You are required to find any position x(1≤ x ≤ N) such that :

(A[1]+A[2]+...A[x-1]) + (A[x+1]+A[x+2]+...A[N]) = S

If there are multiple such positions x, print any such position. If there is no such position, print -1.

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

• First line will contain T, number of testcases. Then the testcases follow.
• Each testcase contains of a single line of input, two integers N, S.

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

For each testcase, output the required position or -1 in case there is no such position.

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

$1 ≤ T ≤ 1000$
$2 ≤ N ≤ 10^{9}$
$1 ≤ S ≤ 10^{18}$

----- Sample Input 1 ------
3
4 8
5 10
2 3

----- Sample Output 1 ------
2
5
-1

----- explanation 1 ------
Test Case $1$: $A[1]+A[3]+A[4]=1+3+4=8$, so $x=2$ is a suitable position.

Test Case $3$: There is no suitable position.

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