You are given three integers n, pos, and k.
There are n people standing in a line indexed from 0 to n - 1. Each person independently chooses a direction:
'L': visible only to people on their right'R': visible only to people on their leftpos sees others as follows:
i < pos is visible if and only if they choose 'L'.i > pos is visible if and only if they choose 'R'.Return the number of possible direction assignments such that the person at index pos sees exactly k people.
Since the answer may be large, return it modulo 109 + 7.
Example 1:
Input: n = 3, pos = 1, k = 0
Output: 2
Explanation:
pos = 1, and index 2 is to the right of pos = 1.k = 0 people, index 0 must choose 'R' and index 2 must choose 'L', keeping both invisible.'L' or 'R' since it does not affect the count. Thus, the answer is 2.Example 2:
Input: n = 3, pos = 2, k = 1
Output: 4
Explanation:
pos = 2, and there is no index to the right.k = 1 person, exactly one of index 0 or index 1 must choose 'L', and the other must choose 'R'.'L' or 'R' since it does not affect the count. Thus, the answer is 2 + 2 = 4.Example 3:
Input: n = 1, pos = 0, k = 0
Output: 2
Explanation:
pos = 0.k = 0 people, no additional condition is required.'L' or 'R'. Thus, the answer is 2.Constraints:
1 <= n <= 1050 <= pos, k <= n - 1Loading editor...
3 1 0