MOD = 998244353i64 def inv(v : Int64) pow(v, MOD - 2) end def pow(v : Int64, p) ret = 1i64 while p > 0 if (p & 1i64) != 0 ret *= v ret %= MOD end v *= v v %= MOD p >>= 1 end ret end n64, k = read_line.split.map(&.to_i64) n = n64.to_i inv5 = inv(5i64) inv5_3 = inv5 * 3 % MOD inv5_4 = inv5 * 4 % MOD mat = Matrix(Int64).new(n * 4, n * 4) (n * 4 - 1).times do |i| mat.a[i + 1][i] = inv5 if i % 4 == 0 mat.a[0][i] = inv5_4 else mat.a[0][i] = inv5_3 mat.a[1][i] = inv5 end end mat.a[0][n * 4 - 1] = inv5_3 mat.a[1][n * 4 - 1] = inv5 mat = mat.pow(k - 1) puts mat.a[n * 4 - 1][0] * inv5 % MOD class Matrix(T) @a : Array(Array(T)) getter :a, :d1, :d2 def initialize(n : Int32, m : Int32) @a = Array.new(n) { Array.new(m, T.zero) } @d1 = n @d2 = m end def clone ret = Matrix(T).new(@d1, @d2) @d1.times do |i| @d2.times do |j| ret.a[i][j] = @a[i][j] end end return ret end def [](idx : Int32) return @a[idx] end def mul(other : Matrix(T)) if @d2 != other.d1 raise ArgumentError.new end d3 = other.d2 tmp = Array.new(d3) { Array.new(@d2, T.zero) } d3.times do |i| tr1 = tmp[i] @d2.times do |j| tr1[j] = other[j][i] end end ret = Array.new(@d1) { Array.new(d3, T.zero) } @d1.times do |i| row1 = @a[i] ret1 = ret[i] d3.times do |j| sum = T.zero row2 = tmp[j] @d2.times do |k| sum += row1[k] * row2[k] sum %= MOD end ret1[j] = sum end end @a = ret end def mul_l(other : Matrix(T)) # in-place if other.d2 != @d1 raise ArgumentError.new end d3 = @d2 tmp = Array.new(d3) { Array.new(@d1, T.zero) } d3.times do |i| tr1 = tmp[i] @d1.times do |j| tr1[j] = @a[j][i] end end other.d1.times do |i| row1 = other.a[i] ret1 = @a[i] d3.times do |j| sum = T.zero row2 = tmp[j] other.d2.times do |k| sum += row1[k] * row2[k] sum %= MOD end ret1[j] = sum end end end def pow(p : Int64) b = Matrix(T).new(@d1, @d2) ret = Matrix(T).new(@d1, @d2) @d1.times do |i| @d2.times do |j| b.a[i][j] = @a[i][j] % MOD end ret.a[i][i] = 1 end while p > 0 if (p & 1) != 0 ret.mul_l(b) end b.mul(b) p >>= 1 end return ret end end