When Vova arrived in Guangzhou, his Chinese friends immediately invited him to a restaurant. Overall n people came to the restaurant, including Vova. The waiter offered to seat the whole company at a traditional large round table with a rotating dish plate in the center.

As Vova was a guest, he got the honorable place by the door. Then m people in the company stated that they wanted to sit near a certain person. Your task is to determine the number of available arrangements to seat Vova's friends at the table.

The first line contains integers n and m (2 ≤ n ≤ 100; 0 ≤ m ≤ n). The next m lines contain integers k₁, …, k_m, where k_i is the number of the person who the person number i wants to sit with (1 ≤ k_i ≤ n; k_i ≠ i). Being an honorable guest, Vova got number 1. His friends are numbered with integers from 2 to n.

Print the number of available arrangements to seat Vova's friends modulo 10⁹ + 7.