B"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 <= n <= 3000 , 1 <= D <= 10^9 ). The remaining n-1 lines each contain a single positive integer, where the i -th line contains the integer p_i ( 1 <= p_i <= 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 . 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) . "...