# Cowmpany Cowmpensation

## 题目描述

Allen, having graduated from the MOO Institute of Techcowlogy (MIT), has started a startup! Allen is the president of his startup. He also hires \$ n-1 \$ other employees, each of which is assigned a direct superior. If \$ u \$ is a superior of \$ v \$ and \$ v \$ is a superior of \$ w \$ then also \$ u \$ is a superior of \$ w \$ . Additionally, there are no \$ u \$ and \$ v \$ such that \$ u \$ is the superior of \$ v \$ and \$ v \$ is the superior of \$ u \$ . Allen himself has no superior. Allen is employee number \$ 1 \$ , and the others are employee numbers \$ 2 \$ through \$ n \$ . Finally, Allen must assign salaries to each employee in the company including himself. Due to budget constraints, each employee's salary is an integer between \$ 1 \$ and \$ D \$ . Additionally, no employee can make strictly more than his superior. Help Allen find the number of ways to assign salaries. As this number may be large, output it modulo \$ 10^9 + 7 \$ .

## 输入输出格式

### 输入格式

The first line of the input contains two integers \$ n \$ and \$ D \$ ( \$ 1 \le n \le 3000 \$ , \$ 1 \le D \le 10^9 \$ ). The remaining \$ n-1 \$ lines each contain a single positive integer, where the \$ i \$ -th line contains the integer \$ p_i \$ ( \$ 1 \le p_i \le i \$ ). \$ p_i \$ denotes the direct superior of employee \$ i+1 \$ .

### 输出格式

Output a single integer: the number of ways to assign salaries modulo \$ 10^9 + 7 \$ .

## 输入输出样例

### 输入样例 #1

``````3 2
1
1
``````

### 输出样例 #1

``````5
``````

### 输入样例 #2

``````3 3
1
2
``````

### 输出样例 #2

``````10
``````

### 输入样例 #3

``````2 5
1
``````

### 输出样例 #3

``````15
``````

## 说明

In the first sample case, employee 2 and 3 report directly to Allen. The three salaries, in order, can be \$ (1,1,1) \$ , \$ (2,1,1) \$ , \$ (2,1,2) \$ , \$ (2,2,1) \$ or \$ (2,2,2) \$ . In the second sample case, employee 2 reports to Allen and employee 3 reports to employee 2. In order, the possible salaries are \$ (1,1,1) \$ , \$ (2,1,1) \$ , \$ (2,2,1) \$ , \$ (2,2,2) \$ , \$ (3,1,1) \$ , \$ (3,2,1) \$ , \$ (3,2,2) \$ , \$ (3,3,1) \$ , \$ (3,3,2) \$ , \$ (3,3,3) \$ .