Permutation *p* is an ordered set of integers *p*<sub class="lower-index">1</sub>,  *p*<sub class="lower-index">2</sub>,  ...,  *p*<sub class="lower-index">*n*</sub>, consisting of *n* distinct positive integers, each of them doesn't exceed *n*. We'll denote the *i*-th element of permutation *p* as *p*<sub class="lower-index">*i*</sub>. We'll call number *n* the size or the length of permutation *p*<sub class="lower-index">1</sub>,  *p*<sub class="lower-index">2</sub>,  ...,  *p*<sub class="lower-index">*n*</sub>.

We'll call position *i* (1 ≤ *i* ≤ *n*) in permutation *p*<sub class="lower-index">1</sub>, *p*<sub class="lower-index">2</sub>, ..., *p*<sub class="lower-index">*n*</sub> good, if |*p*[*i*] - *i*| = 1. Count the number of permutations of size *n* with exactly *k* good positions. Print the answer modulo 1000000007 (10<sup class="upper-index">9</sup> + 7).
The single line contains two space-separated integers *n* and *k* (1 ≤ *n* ≤ 1000, 0 ≤ *k* ≤ *n*).
print(1)
print(1)
print(1)
print(1)