// Hunter Schafer, CSE 143
// Examples of recursive backtracking

import java.util.*;

public class Backtracking2 {
    public static void main(String[] args) {
        diceSum(2, 7);
    }

    // Prints all possible outcomes of rolling the given
    // number of six-sided dice that add up to exactly
    // the given sum, in [#, #, #] format.
    public static void diceSum(int dice, int sum) {
        diceSum(dice, sum, 0, new ArrayList<Integer>());
    }

    // Prints all the possible outcomes of rolling the given number
    // of six-sided dice that add up to exactly the given sum, in [#, #, #] format.
    // sumSoFar is the sum of all the numbers in chosen. chosen is
    // the prefix for all the answers printed.
    private static void diceSum(int dice, int sum, int sumSoFar, List<Integer> chosen) {
        if (dice == 0 && sumSoFar == sum) {
            System.out.println(chosen);
        } else if (sumSoFar + dice <= sum && sumSoFar + 6 * dice >= sum) {
            // The check above makes sure
            //    1. The sum is attainable from sumSoFa
            //    2. We won't overshoot the target sum with the number of dice remaining

            for (int i = 1; i <= 6; i++) {                     // for all possible choices
                chosen.add(i);                                 //     choose
                diceSum(dice - 1, sum, sumSoFar + i, chosen);  //     explore
                chosen.remove(chosen.size() - 1);              //     unchoose
            }
        }
    }
}