You are given two positive integers startPos and endPos. Initially, you are standing at position startPos on an infinite number line. With one step, you can move either one position to the left, or one position to the right.
Given a positive integer k, return the number of different ways to reach the position endPos starting from startPos, such that you perform exactly k steps. Since the answer may be very large, return it modulo 109 + 7.
Two ways are considered different if the order of the steps made is not exactly the same.
\n\nNote that the number line includes negative integers.
\n\n\n
Example 1:
\n\n\nInput: startPos = 1, endPos = 2, k = 3\nOutput: 3\nExplanation: We can reach position 2 from 1 in exactly 3 steps in three ways:\n- 1 -> 2 -> 3 -> 2.\n- 1 -> 2 -> 1 -> 2.\n- 1 -> 0 -> 1 -> 2.\nIt can be proven that no other way is possible, so we return 3.\n\n
Example 2:
\n\n\nInput: startPos = 2, endPos = 5, k = 10\nOutput: 0\nExplanation: It is impossible to reach position 5 from position 2 in exactly 10 steps.\n\n\n
\n
Constraints:
\n\n1 <= startPos, endPos, k <= 1000给你两个 正 整数 startPos 和 endPos 。最初，你站在 无限 数轴上位置 startPos 处。在一步移动中，你可以向左或者向右移动一个位置。
给你一个正整数 k ，返回从 startPos 出发、恰好 移动 k 步并到达 endPos 的 不同 方法数目。由于答案可能会很大，返回对 109 + 7 取余 的结果。
如果所执行移动的顺序不完全相同，则认为两种方法不同。
\n\n注意：数轴包含负整数。
\n\n\n\n
示例 1：
\n\n输入：startPos = 1, endPos = 2, k = 3\n输出：3\n解释：存在 3 种从 1 到 2 且恰好移动 3 步的方法：\n- 1 -> 2 -> 3 -> 2.\n- 1 -> 2 -> 1 -> 2.\n- 1 -> 0 -> 1 -> 2.\n可以证明不存在其他方法，所以返回 3 。\n\n
示例 2：
\n\n输入：startPos = 2, endPos = 5, k = 10\n输出：0\n解释：不存在从 2 到 5 且恰好移动 10 步的方法。\n\n
\n\n
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