B'You are given an integer n . For each (m, k) such that 3 <= q m <= q n+1 and 0 <= q k <= q n-1 , count the permutations of [1, 2, ..., n] such that p_i + p_{i+1} geq m for exactly k indices i , modulo 998 ,244 ,353 . The input consists of a single line, which contains two integers n , x ( 2 <= q n <= q 4000 , 1 <= q x < 1 ,000 ,000 ,007 ). Let a_{m,k} be the answer for the pair (m, k) , modulo 998 ,244 ,353 . Let large S = sum_{m=3}^{n+1} sum_{k=0}^{n-1} a_{m,k}x^{mn+k} phantom{0}. Output a single line with an integer: S modulo 1 ,000 ,000 ,007 . Note that using two different modulos is intentional. We want you to calculate all the a_{m,k} modulo 998 ,244 ,353 , then treat them like integers in the range [0, 998 ,244 ,352] , and hash them modulo 1 ,000 ,000 ,007 . In the first test case, the answers for all (m, k) are shown in the following table: Therefore, the value to print is 2^9 cdot 0 + 2^{10} cdot 0 + 2^{11} cdot 6 + 2^{12} cdot 0 + 2^{13} cdot 4 + 2^{14} cdot 2 equiv 77 ,824 phantom{0} ( text{mod} phantom{0} 1 ,000 ,000 ,007) . In the second test case, the answers for all (m, k) are shown in the following table: In the third test case, the answers for all (m, k) are shown in the following table: '...