Preparando MOJI
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 $$$10^9 + 7$$$.
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 $$$i+1$$$.
Output a single integer: the number of ways to assign salaries modulo $$$10^9 + 7$$$.
3 2
1
1
5
3 3
1
2
10
2 5
1
15
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 $$$(1,1,1)$$$, $$$(2,1,1)$$$, $$$(2,2,1)$$$, $$$(2,2,2)$$$, $$$(3,1,1)$$$, $$$(3,2,1)$$$, $$$(3,2,2)$$$, $$$(3,3,1)$$$, $$$(3,3,2)$$$, $$$(3,3,3)$$$.
Informação
Provedor Codeforces
Código CF995F
Tags
Submetido 0
BOUA! 0
Taxa de BOUA's 0%
Datas 09/05/2023 09:35:20
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