Given an integer array with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target.

Example:

nums = [1, 2, 3]target = 4The possible combination ways are:(1, 1, 1, 1)(1, 1, 2)(1, 2, 1)(1, 3)(2, 1, 1)(2, 2)(3, 1)Note that different sequences are counted as different combinations.Therefore the output is 7.

Follow up:
What if negative numbers are allowed in the given array?
How does it change the problem?
What limitation we need to add to the question to allow negative numbers?

Credits:
Special thanks to @pbrother for adding this problem and creating all test cases.

public class Solution {    public int combinationSum4(int[] nums, int target) {        if (nums.length==0) return 0;        Arrays.sort(nums);        int[] combines = new int[target+1];        combines[0] = 1;        for (int val=1;val<=target;val++)            for (int i=0;i<nums.length;i++)                if (val >= nums[i]){                    combines[val] += combines[val-nums[i]];                } else break;        return combines[target];    }}

LeetCode-Combination Sum IV