def solve(io) n, m, k = io.get3 l, r = io.get2_c(m); l.map!(&.- 1); r.map!(&.- 1) dp = Array.new_md(k+1, n+1, Mint.zero) dp[0][0] = Mint.new(1) k.times do |ki| dpc = CumulativeSum.new(dp[ki]) m.times do |mi| dp[ki+1][l[mi]] += dpc[l[mi]..r[mi]] dp[ki+1][r[mi]+1] -= dpc[l[mi]..r[mi]] end n.times do |ni| dp[ki+1][ni+1] += dp[ki+1][ni] end end io.put dp[k][n-1] 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 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 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 CumulativeSum(T) def initialize(a : Array(T)) @n = a.size @s = Array.new(@n+1, T.additive_identity) @n.times.each do |i| @s[i+1] = @s[i] + a[i] end end getter n : Int32 def [](r : Range) sc = Indexable.range_to_index_and_count(r, @n) raise ArgumentError.new("Invalid range") if sc.nil? start, count = sc @s[start + count] - @s[start] end @s : 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 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)