B'Koishi is unconsciously permuting n numbers: 1, 2, ldots, n . She thinks the permutation p is beautiful if s= sum limits_{i=1}^{n-1} [p_i+1=p_{i+1}] . [x] equals to 1 if x holds, or 0 otherwise. For each k in[0,n-1] , she wants to know the number of beautiful permutations of length n satisfying k= sum limits_{i=1}^{n-1}[p_i<p_{i+1}] . There is one line containing two intergers n ( 1 <= q n <= q 250 ,000 ) and s ( 0 <= q s < n ). Print one line with n intergers. The i -th integers represents the answer of k=i-1 , modulo 998244353 . Let f(p)= sum limits_{i=1}^{n-1}[p_i<p_{i+1}] . Testcase 1: [2,1] is the only beautiful permutation. And f([2,1])=0 . Testcase 2: Beautiful permutations: [1,2,4,3] , [1,3,4,2] , [1,4,2,3] , [2,1,3,4] , [2,3,1,4] , [3,1,2,4] , [3,4,2,1] , [4,2,3,1] , [4,3,1,2] . The first six of them satisfy f(p)=2 , while others satisfy f(p)=1 . '...