def solve(io) n = io.get a = io.get_a(n) f = Fact(Mint).new(n) r = Mint.zero a.each_with_index do |ai, i| r += f.combi(n-1, i) * ai end io.put r end class ProconIO def initialize(@ins : IO = STDIN, @outs : IO = STDOUT) @buf = IO::Memory.new("") end def get(k : T.class = Int32) forall T get_v(k) end macro define_get {% for i in (2..9) %} def get({{ *(1..i).map { |j| "k#{j}".id } }}) { {{ *(1..i).map { |j| "get(k#{j})".id } }} } end {% end %} end define_get macro define_getn {% for i in (2..9) %} def get{{i}}(k : T.class = Int32) forall T get({{ *(1..i).map { "k".id } }}) end {% end %} end define_getn def get_a(n : Int, k : T.class = Int32) forall T Array.new(n) { get_v(k) } end def get_c(n : Int, k : T.class = Int32) forall T get_a(n, k) end macro define_get_c {% for i in (2..9) %} def get_c(n : Int, {{ *(1..i).map { |j| "k#{j}".id } }}) a = Array.new(n) { get({{ *(1..i).map { |j| "k#{j}".id } }}) } { {{ *(1..i).map { |j| "a.map { |e| e[#{j-1}] }".id } }} } end {% end %} end define_get_c macro define_getn_c {% for i in (2..9) %} def get{{i}}_c(n : Int, k : T.class = Int32) forall T get_c(n, {{ *(1..i).map { "k".id } }}) end {% end %} end define_getn_c def get_m(r : Int, c : Int, k : T.class = Int32) forall T Array.new(r) { get_a(c, k) } end macro define_put {% for i in (1..9) %} def put({{ *(1..i).map { |j| "v#{j}".id } }}, *, delimiter = " ") {% for j in (1..i) %} print_v(v{{j}}, delimiter) {% if j < i %}@outs << delimiter{% end %} {% end %} @outs.puts end {% end %} end define_put def put_e(*vs) put(*vs) exit end def put_f(*vs) put(*vs) @outs.flush end private def get_v(k : Int32.class); get_token.to_i32; end private def get_v(k : Int64.class); get_token.to_i64; end private def get_v(k : UInt32.class); get_token.to_u32; end private def get_v(k : UInt64.class); get_token.to_u64; end private def get_v(k : Float64.class); get_token.to_f64; end private def get_v(k : String.class); get_token; end private def get_token loop do token = @buf.gets(' ', chomp: true) break token unless token.nil? @buf = IO::Memory.new(@ins.read_line) end end private def print_v(v, dlimiter) @outs << v end private def print_v(v : Enumerable, delimiter) v.each_with_index do |e, i| @outs << e @outs << delimiter if i < v.size - 1 end end end struct Int def cdiv(b : Int) (self + b - 1) // b end def bit?(i : Int) bit(i) == 1 end def set_bit(i : Int) self | (self.class.new(1) << i) end def reset_bit(i : Int) self & ~(self.class.new(1) << i) end {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.34.0") < 0 %} def bit_length : Int32 x = self < 0 ? ~self : self if x.is_a?(Int::Primitive) Int32.new(sizeof(self) * 8 - x.leading_zeros_count) else to_s(2).size end end {% end %} end struct Int32 SQRT_MAX = 46_340_i32 def isqrt m = SQRT_MAX r = (1_i32..SQRT_MAX).bsearch { |i| i**2 > self } r.nil? ? SQRT_MAX : r - 1 end end struct Int64 SQRT_MAX = 3_037_000_499_i64 def isqrt r = (1_i64..SQRT_MAX).bsearch { |i| i**2 > self } r.nil? ? SQRT_MAX : r - 1 end end struct Float64 def near_zero? self.abs < EPSILON end end struct Number {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "1.1.0") < 0 %} def zero? self == 0 end def positive? self > 0 end def negative? self < 0 end {% end %} {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.36.0") < 0 %} def self.additive_identity zero end def self.multiplicative_identity new(1) end {% end %} end class Array macro new_md(*args, &block) {% if !block %} {% for arg, i in args[0...-2] %} Array.new({{arg}}) { {% end %} Array.new({{args[-2]}}, {{args[-1]}}) {% for arg in args[0...-2] %} } {% end %} {% else %} {% for arg, i in args %} Array.new({{arg}}) { |_i{{i}}| {% end %} {% for block_arg, i in block.args %} {{block_arg}} = _i{{i}} {% end %} {{block.body}} {% for arg in args %} } {% end %} {% end %} end end macro min_u(a, b) {{a}} = Math.min({{a}}, {{b}}) end macro max_u(a, b) {{a}} = Math.max({{a}}, {{b}}) end macro zip(a, *b, &block) {{a}}.zip({{*b}}) {{block}} end class Fact(T) def initialize(@n : Int32) @table = Array.new(@n+1, T.multiplicative_identity) (1..@n).each do |i| @table[i] = @table[i-1] * i end @inv_table = Array.new(@n+1, T.multiplicative_identity) @inv_table[@n] //= @table[@n] (1..@n).reverse_each do |i| @inv_table[i-1] = @inv_table[i] * i end end getter table : Array(T) getter inv_table : Array(T) def fact(n : Int) @table[n] end def perm(n : Int, r : Int) @table[n] * @inv_table[n-r] end def combi(n : Int, r : Int) @table[n] * @inv_table[r] * @inv_table[n-r] end def homo(n : Int, r : Int) combi(n + r - 1, r) end @table : Array(T) @inv_table : Array(T) end def powr(a : T, n : Int, i : T = T.multiplicative_identity) forall T powr(a, n, i) { |a, b| a * b } end def powr(a : T, n : Int, i : T = T.multiplicative_identity, &block) forall T return i if n == 0 r, b = i, a while n > 0 r = yield r, b if n.bit(0) == 1 b = yield b, b n >>= 1 end r end def ext_gcd(a : T, b : T) forall T if a == 0 {b, T.new(0), T.new(1)} else g, x, y = ext_gcd(b % a, a) {g, y - (b // a) * x, x} end end def bit_subsets(a : Int, includes_zero = false) n = i = a if includes_zero while i >= 0 yield i & n i = (i & n) - 1 end else while i > 0 yield i i = (i - 1) & n end end end def bit_zeta_trans_subset(n : Int, f : Array(T), &compose : (T, T) -> T) forall T g = Array.new(1 << n) { |i| f[i] } n.times do |i| (1 << n).times do |j| if j >> i & 1 != 0 g[j] = compose.call(g[j], g[j ^ (1 << i)]) end end end g end def bit_zeta_trans_superset(n : Int, f : Array(T), &compose : (T, T) -> T) forall T g = Array.new(1 << n) { |i| f[i] } n.times do |i| (1 << n).times do |j| if j >> i & 1 == 0 g[j] = compose.call(g[j], g[j ^ (1 << i)]) end end end g end abstract struct ModInt < Number macro new_type(name, mod) struct {{name}} < ModInt @@mod : Int32 = {{mod}} end end def initialize(v : Int) @v = (v % @@mod).to_i64 end def_hash @@mod, @v def to_s @v.to_s end def to_s(io : IO) : Nil @v.to_s(io) end getter v : Int64 delegate to_i, to: @v def ==(r : self) @v == r.v end def ==(r : Int) @v == (r % @@mod) end def - : self m(-@v) end def +(r : self) m(@v + r.v) end def +(r : Int) self + m(r) end def -(r : self) m(@v - r.v) end def -(r : Int) self - m(r) end def *(r : self) m(@v * r.v) end def *(r : Int) self * m(r) end def //(r : self) self * r.inv end def //(r : Int) self // m(r) end def **(n : Int) powr(self, n) end def inv m(ext_gcd(@v.to_i32, @@mod)[1]) end private def m(v : Int) self.class.new(v) end end ModInt.new_type(Mint, 10**9+7) solve(ProconIO.new)