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/**
 * Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.
 * For example,
 * If n = 4 and k = 2, a solution is:
 * [
      [2,4],
      [3,4],
      [2,3],
      [1,2],
      [1,3],
      [1,4],
    ]
 */
 
 public class Solution {
    public ArrayList<ArrayList<Integer>> combine(int n, int k) {
        if(n < k)
            return null;
        ArrayList<ArrayList<Integer>> res = new ArrayList<ArrayList<Integer>>();
        if(k == 1){
            for(int i = 1; i <= n; i++){
                ArrayList<Integer> arr = new ArrayList<Integer>();
                arr.add(i);
                res.add(arr);
            }
            return res;
        }
        for(int i = n; i>= k; i--){
            for(ArrayList<Integer> arr : combine(i - 1, k - 1)){
                arr.add(i);
                res.add(arr);
            }
        }
        return res;
    }
    
    
    public List<List<Integer>> combineAnother(int n, int k) {
        List<List<Integer>> res = new ArrayList<List<Integer>>();
        if(k > n || k <= 0) return res;
        helper(n, k, 1, new ArrayList<Integer>(), res);
        return res;
    }
    public void helper(int n, int k, int start, List<Integer> path, List<List<Integer>> res) {
        if(k < 0) return;
        if(k == 0) res.add(path);
        for(int i = start; i <= n; i++) {
            List<Integer> tmp = new ArrayList<Integer>(path);
            tmp.add(i);
            helper(n, k - 1, i + 1, tmp, res);
        }
    }
 }