All Tracks Math Number Theory Basic Number Theory-1 Problem

Panda and Chain Reaction
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Ad-Hoc, Basic Programming, Mathematics, Modular exponentiation, Number Theory

Problem
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Panda has become a scientist recently. In his laboratory, there are infinite number of chambers where a chamber number K is connected to a chamber number K-1.

The numbering of chambers start from 0. Initially, X number of particles are present in the chamber number 0. The number of particles present in chamber K is K times the number of particles present in chamber K-1. You are supposed to help Panda in finding out the number of particles in a given chamber number N.

Note: The number of particles in chamber K cannot be calculated until the number of particles in chamber K-1 are calculated.

Input Format:

The first line will contain the integer T, the number of test cases. Each test case consists of two space separated integers N and X.

Output Format:

For each test case, output the answer to Panda's query. Since the output can be very large, output the answer modulo 106+3.

Constraints:

1 <= T <= 105

  • Subtask 1: (20 points)
    1 <= N, X <= 105

  • Subtask 2: (80 points)
    1 <= N, X <= 1018

SAMPLE INPUT
2
1 3
2 1
SAMPLE OUTPUT
3
2
Explanation

Case 1: For first test case, initially there were 3 particles. In Chamber K=1, the number of particles became 1*3 = 3.

Case 2: Initially, there is only 1 particle. In Chamber K=1, the number of particle became 1*1 = 1. In Chamber K=2, the number of particle became 2*1 = 2.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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