public class DifferenceEngine {

	public static int f(int x, int[] coefficients) {
		int sum = 0;
		for (int i = 0; i < coefficients.length; i++) {
			int p = coefficients.length - i - 1;
			sum += coefficients[i] * Math.pow(x, p);
		}
		return sum;
	}

	public static void main(String[] args) {
		// f(x) = ax^n + bx^(n-1) ...
		// The coefficients a,b.. are listed here:
		int[] coefficients = { 1, 0, 4 };
		// This example is x^2 + 0 x + 4

		// n is the largest power (x^2 in this example)
		int n = coefficients.length - 1;

		int x = 3;
		int max_x = 6;

		// Initialize the differences
		int[] diffs = new int[n + 1];
		for (int i = 0; i < n + 1; i++) {
			int x0 = x - n + i;
			int fx = f(x0, coefficients);
			int diff = fx - diffs[0];
			diffs[0] = fx;

			for (int j = 1; j <= i; j++) {
				int d2 = diff - diffs[j];
				diffs[j] = diff;
				diff = d2;
			}
		}

		// Actual Difference Engine Simulation
		// (you don't have to simulate the above part)
		while (x < max_x) {
			int i = diffs.length - 1;
			while (i > 0) {
				int d = diffs[i];
				i -= 1;
				diffs[i] += d;
			}

			x++;
			System.out.println(x + " " + diffs[0]);
		}

	}

}