# Time:  O(k * C(n, k))
# Space: O(k)
#
# Find all possible combinations of k numbers that add up to a number n,
# given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.
#
# Ensure that numbers within the set are sorted in ascending order.
#
#
# Example 1:
#
# Input: k = 3, n = 7
#
# Output:
#
# [[1,2,4]]
#
# Example 2:
#
# Input: k = 3, n = 9
#
# Output:
#
# [[1,2,6], [1,3,5], [2,3,4]]
#

class Solution:
    # @param {integer} k
    # @param {integer} n
    # @return {integer[][]}
    def combinationSum3(self, k, n):
        result = []
        self.combinationSumRecu(result, [], 1, k, n)
        return result
    
    def combinationSumRecu(self, result, intermediate, start, k, target):
        if k == 0 and target == 0:
            result.append(list(intermediate))
        elif k < 0:
            return
        while start < 10 and start * k + k * (k - 1) / 2 <= target:
            intermediate.append(start)
            self.combinationSumRecu(result, intermediate, start + 1, k - 1, target - start)
            intermediate.pop()
            start += 1
