Description: Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1, p2, ..., pn. We'll call position i (1 ≤ i ≤ n) in permutation p1, p2, ..., pn good, if |p[i] - i| = 1. Count the number of permutations of size n with exactly k good positions. Print the answer modulo 1000000007 (109 + 7). Input Format: The single line contains two space-separated integers n and k (1 ≤ n ≤ 1000, 0 ≤ k ≤ n). Output Format: Print the number of permutations of length n with exactly k good positions modulo 1000000007 (109 + 7). Note: The only permutation of size 1 has 0 good positions. Permutation (1, 2) has 0 good positions, and permutation (2, 1) has 2 positions. Permutations of size 3: 1. (1, 2, 3) — 0 positions 2. $$(1,3,2)$$ — 2 positions 3. $$(2,1,3)$$ — 2 positions 4. $$(2,3,1)$$ — 2 positions 5. $$(3,1,2)$$ — 2 positions 6. (3, 2, 1) — 0 positions