## CODESPTH - Polygon Diagonals

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 <= 10^9

1 <= K <= N

**Sample Input:**

3

4 1

5 2

5 3

**Sample 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.

Added by: | Varun Jalan |

Date: | 2011-10-18 |

Time limit: | 1s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | own problem used for CodeSprint - InterviewStreet Contest |