PERIODNI - Periodni

给定一个N列的表格，底部对齐，然后向表格中填入K个相同的数，填写时要求不能有两个数在同一列，或同一行，下图中b是错误的填写，a是正确的填写，因为两个a虽然在同一行，但它们中间的表格断开。 输出所有填写方案数对1 000 000 007的余数。 输入：
第一行两个整数 N 和 K (1 ≤ N ≤ 500, 1 ≤ K ≤ 500),表示表格的列数和要填写的数的个数。
接下来一行N个数，表示每列的高度。高度不超过 1 000 000. 输出：
一个整数，方案总数对1000 000 007的余数。 注意：
对于 40% 的数据, 所有数值小于15.
对于70% 的数据，所有数值小于100. Translated by @yijan

[English](/problems/PERIODNI/en/) [Vietnamese](/problems/PERIODNI/vn/)Luka is bored in chemistry class so he is staring at a large periodic table of chemical elements hanging from a wall above the blackboard. To kill time, Luka decided to make his own table completely different from the one in the classroom. His table consists of N columns, each with some height, aligned at the bottom (see example below). After he draws the table he needs to fill it with elements. He first decided to enter the noble gases of which there are K. Luka must put them in the table so that no two noble gases are close to each other. Two squares in the table are close to each other if they are in the same column or row, and all squares between them exist. In the example below, the 'a' squares are not close, but the 'b' squares are.  Write a program that, given N, K and the heights of the N columns, calculates the total number of ways for Luka to place the noble gases into the table. This number can be large, so output it modulo 1 000 000 007.

The first line contains the integers N and K separated by a space (1 The next line contains N positive integers, separated by spaces. These are heights of the columns from left to right. The heights will be at most 1 000 000.

Output the number of ways for Luka to fill his table with noble gases, modulo 1 000 000 007.

5 2
2 3 1 2 4

43