Problem:
Score : 600 points

Problem Statement

Consider the following arithmetic progression with n terms:

x, x + d, x + 2d, \ldots, x + (n-1)d

What is the product of all terms in this sequence?
Compute the answer modulo 1\ 000\ 003.

You are given Q queries of this form.
In the i-th query, compute the answer in case x = x_i, d = d_i, n = n_i.

Constraints

1 \leq Q \leq 10^5

0 \leq x_i, d_i \leq 1\ 000\ 002

1 \leq n_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

Q
x_1 d_1 n_1
:
x_Q d_Q n_Q

Output

Print Q lines.

In the i-th line, print the answer for the i-th query.

Sample Input 1

2
7 2 4
12345 67890 2019

Sample Output 1

9009
916936

For the first query, the answer is 7 \times 9 \times 11 \times 13 = 9009.
Don't forget to compute the answer modulo 1\ 000\ 003.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.math.BigDecimal;
import java.math.BigInteger;

public class Main {
    private static final StringBuilder builder = new StringBuilder();
    public static void main(String[] args) {

        double mod = 1000003;
        int q = readInt();

        for (int i = 0; i < q; i++) {
            double x = readDouble(), d = readDouble(), n = readDouble();
            double m = 1;

            for (int j = 0; j < n; j++) {
                m = (m * ((x + (j * d) % mod) % mod)) % mod;
            }

            System.out.println((long) m);
            System.gc();
        }
    }

    private static void read() {
        builder.setLength(0);
        while (true) {
            try {
                int b = System.in.read();
                if (b == ' ' || b == '\n' || b == -1) {
                    break;
                } else {
                    builder.appendCodePoint(b);
                }
            } catch (IOException e) {
                break;
            }
        }
    }

    private static int readInt() {
        read();
        return Integer.parseInt(builder.toString());
    }

    private static int readInt(int radix) {
        read();
        return Integer.parseInt(builder.toString(), radix);
    }

    private static long readLong() {
        read();
        return Long.parseLong(builder.toString());
    }

    private static long readLong(int radix) {
        read();
        return Long.parseLong(builder.toString(), radix);
    }

    private static BigInteger readBigInteger() {
        read();
        return new BigInteger(builder.toString());
    }

    private static BigInteger readBigInteger(int radix) {
        read();
        return new BigInteger(builder.toString(), radix);
    }

    private static double readDouble() {
        read();
        return Double.parseDouble(builder.toString());
    }

    private static BigDecimal readBigDecimal() {
        read();
        return new BigDecimal(builder.toString());
    }

    private static float readFloat() {
        read();
        return Float.parseFloat(builder.toString());
    }

    private static void skipLine() {
        while (true) {
            try {
                int b = System.in.read();
                if (b == '\n' || b == -1) {
                    break;
                }
            } catch (IOException e) {
                break;
            }
        }
    }

    private static void skip() {
        while (true) {
            try {
                int b = System.in.read();
                if (b == ' ' || b == '\n' || b == -1) break;
            } catch (IOException e) {
                break;
            }
        }
    }

}