Consider a regular polygon with N vertices labelled 1..N. In how many ways can you draw K diagonals such that no two diagonals intersect at a point strictly inside the polygon? A diagonal is a line segment joining two non adjacent vertices of the polygon.

Input

The first line contains the number of test cases T. Each of the next T lines contain two integers N and K.

Output

Output T lines, one corresponding to each test case. Since the answer can be really huge, output it modulo 1000003.

Constraints

1 ≤ T ≤ 10000

4 ≤ N ≤ 10⁹

1 ≤ K ≤ N

Example

Input:
3
4 1
5 2
5 3
Output:
2
5
0

Explanation

For the first case, there are clearly 2 ways to draw 1 diagonal - 1 to 3, or 2 to 4. (Assuming the vertices are labelled 1..N in cyclic order).

For the third case, at most 2 non-intersecting diagonals can be drawn in a 5-gon, and so the answer is 0.