Count Ordered Dice Outcomes With a Given Total

### Problem Roll n dice, each with faces 1 through k. Count ordered outcomes whose sum equals target, and return the count modulo 1000000007. Different choices for individual dice count separately even when they give the same sum. ```cpp class Solution { public: int numRollsToTarget(int n, int k, int target); }; ``` ### Examples **Example 1:** ```text Input: n = 2, k = 3, target = 4 Output: 3 Explanation: The outcomes are(1,3),(2,2),(3,1). ``` **Example 2:** ```text Input: n = 3, k = 2, target = 4 Output: 3 Explanation: Exactly one of the three dice shows2 and the other two show1. ``` ### Constraints - Both n and k are integers in `[1,30]`. - target is an integer between 1 and 1000. ### Contract considerations Dice are distinct positions in an ordered outcome. No unordered-partition interpretation is used. ```hint Read the boundary condition Does swapping the results of two different dice create a different outcome, even when the total is unchanged? ``` ### Boundary reminders Dice are distinct positions in an ordered outcome. No unordered-partition interpretation is used.