CF466D.Increase Sequence

Peter has a sequence of integers _a_1, _a_2, ..., a__n. Peter wants all numbers in the sequence to equal h. He can perform the operation of "adding one on the segment [l, r]": add one to all elements of the sequence with indices from l to r (inclusive). At that, Peter never chooses any element as the beginning of the segment twice. Similarly, Peter never chooses any element as the end of the segment twice. In other words, for any two segments [_l_1, _r_1] and [_l_2, _r_2], where Peter added one, the following inequalities hold: _l_1 ≠ _l_2 and _r_1 ≠ _r_2.

How many distinct ways are there to make all numbers in the sequence equal h? Print this number of ways modulo 1000000007 (109 + 7). Two ways are considered distinct if one of them has a segment that isn't in the other way.

彼得有一个整数序列 $a_1, a_2, \dots, a_n$。彼得希望序列中所有数都等于 $h$。他可以执行“对区间 $[l, r]$ 加一”的操作：将序列中下标从 $l$ 到 $r$（含端点）的所有元素均加一。此外，彼得从不会将任意同一个元素作为两个不同操作区间的左端点；同样，他也从不会将任意同一个元素作为两个不同操作区间的右端点。换言之，对于彼得执行的任意两个加一操作所对应的区间 $[l_1, r_1]$ 和 $[l_2, r_2]$，恒有 $l_1 \ne l_2$ 且 $r_1 \ne r_2$。

有多少种不同的方式能使得序列中所有数都变为 $h$？请输出该方案数对 $1000000007$（即 $10^9 + 7$）取模的结果。若两种方式中存在一个操作区间只出现在其中一种方式中，则认为这两种方式不同。

The first line contains two integers n, h (1 ≤ n, h ≤ 2000). The next line contains n integers _a_1, _a_2, ..., a__n (0 ≤ a__i ≤ 2000).

第一行包含两个整数 $n$ 和 $h$（$1 \leq n, h \leq 2000$）。下一行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \leq a_i \leq 2000$）。

Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

输出一个整数——该问题答案对 $1000000007$（即 $10^9 + 7$）取模的结果。