def solve(io) n, m = io.get2 g = GraphW(Int64).new(n*2, 10_i64**18) m.times do ai, bi, ci = io.get(Int32, Int32, Int64); ai -= 1; bi -= 1 g.add_edge_b(ai, bi, ci) g.add_edge_b(ai+n, bi+n, ci) g.add_edge(ai, bi+n, 0_i64) g.add_edge(bi, ai+n, 0_i64) end n.times do |i| g.add_edge(i, i+n, 0_i64) end d = g.dijkstra(0).dist n.times do |i| io.put d[i] + d[i+n] 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 Number {% 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 class ProconIO def initialize(@ins : IO = STDIN, @outs : IO = STDOUT) @buf = [] of String @index = 0 end def get(k : T.class = Int32) forall T get_v(k) end macro define_get {% for i in (2..9) %} def get( {% for j in (1..i) %} k{{j}}{% if j < i %},{% end %} {% end %} ) { {% for j in (1..i) %} get(k{{j}}){% if j < i %},{% end %} {% end %} } end {% end %} end define_get macro define_getn {% for i in (2..9) %} def get{{i}}(k : T.class = Int32) forall T get( {% for j in (1..i) %} k{% if j < i %}, {% end %} {% end %} ) 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, {% for j in (1..i) %} k{{j}}{% if j < i %},{% end %} {% end %} ) a = Array.new(n) do get( {% for j in (1..i) %} k{{j}}{% if j < i %},{% end %} {% end %} ) end { {% for j in (1..i) %} a.map { |e| e[{{j-1}}] }{% if j < i %},{% end %} {% end %} } 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, {% for j in (1..i) %} k{% if j < i %}, {% end %} {% end %} ) 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 def put(*vs) vs.each.with_index do |v, i| put_v(v) @outs.print i < vs.size - 1 ? " " : "\n" end end def put_e(*vs) put(*vs) exit 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 : String.class); get_token; end private def get_token if @buf.size == @index str = @ins.read_line @buf = str.split @index = 0 end v = @buf[@index] @index += 1 v end private def put_v(vs : Enumerable) vs.each_with_index do |v, i| @outs.print v @outs.print " " if i < vs.size - 1 end end private def put_v(v) @outs.print v end end macro min_u(a, b) {{a}} = Math.min({{a}}, {{b}}) end macro max_u(a, b) {{a}} = Math.max({{a}}, {{b}}) end class Graph alias Node = Int32 def initialize(@n : Node) @g = Array(Array(Node)).new(@n) { [] of Node } end getter n : Node delegate :[], to: @g def add_edge(u : Node, v : Node) @g[u] << v end def add_edge_b(u : Node, v : Node) @g[u] << v @g[v] << u end end class GraphW(T) alias Node = Int32 struct Edge(T) def initialize(@src : Node, @dst : Node, @wt : T) end getter src : Node, dst : Node getter wt : T end def initialize(@n : Node, @inf = 10**9) @g = Array(Array(Edge(T))).new(@n) { [] of Edge(T) } end getter n : Node getter inf : T delegate :[], to: @g def add_edge(u : Node, v : Node, wt : T) @g[u] << Edge.new(u, v, wt) end def add_edge_b(u : Node, v : Node, wt : T) @g[u] << Edge.new(u, v, wt) @g[v] << Edge.new(v, u, wt) end end class Heap(T) def initialize initialize { |a, b| a <=> b } end def initialize(&@cmp : (T, T) -> Int32) dummy = uninitialized T @b = [dummy] end def initialize(a : Array(T)) initialize(a) { |a, b| a <=> b } end def initialize(a : Array(T), &@cmp : (T, T) -> Int32) dummy = uninitialized T @b = [dummy] a.each do |e| push(e) end end def empty? @b.size == 1 end def size @b.size - 1 end def first @b[1] end def first=(v : T) @b[1], i = v, 1 while @b.size > i << 1 l, r = i << 1, i << 1 | 1 j = @b.size <= r || @cmp.call(@b[l], @b[r]) < 0 ? l : r break if @cmp.call(@b[i], @b[j]) < 0 @b[j], @b[i] = @b[i], @b[j] i = j end end def push(v : T) @b.push(v) i = @b.size - 1 while i > 1 j = i >> 1 break if @cmp.call(@b[j], @b[i]) < 0 @b[j], @b[i] = @b[i], @b[j] i = j end self end def pop v, w = @b[1], @b.pop self.first = w unless empty? v end @b : Array(T) end class Dijkstra(T) alias Node = GraphW::Node alias Edge = GraphW::Edge def initialize(@g : GraphW(T), s : Node) n = sent = @g.n @dist = Array.new(n, @g.inf) @dist[s] = T.additive_identity @prev = Array.new(n, sent) se = Edge.new(sent, s, T.new(0)) h = Heap.new([se]) { |a, b| a.wt <=> b.wt } until h.empty? e = h.pop next if @prev[e.dst] != sent @prev[e.dst] = e.src @g[e.dst].each do |f| w = e.wt + f.wt if w < @dist[f.dst] @dist[f.dst] = w h.push(Edge.new(f.src, f.dst, w)) end end end end getter dist : Array(T) @dist : Array(T) @prev : Array(Node) end class GraphW(T) def dijkstra(s) Dijkstra.new(self, s) end end solve(ProconIO.new)