main = -> { N, K = ints fn = (1 .. N).inject(1) { _1 * _2 % MOD }.pow(MOD - 2, MOD) fp = (K .. K + N - 1).inject(1) { _1 * _2 % MOD } ans = 0 exp2 = 1 N.times do |n| ans += exp2 * fp * fn ans %= MOD fp *= (K - 1 - n) * (K + N - 1 - n).pow(MOD - 2, MOD) fp %= MOD exp2 *= 2 exp2 %= MOD end puts ans } DEBUG = true MOD = 10**9+7 YESNO = %w(No Yes) INF = 10**9 require "set" require "prime" def int; gets.to_s.to_i end def ints; gets.to_s.split.map { |s| s.to_i } end def int1s; gets.to_s.split.map { |s| s.to_i - 1 } end def float; gets.to_s.to_f end def floats; gets.to_s.split.map { |s| s.to_f } end def array_of(&convert); gets.to_s.split.map(&convert) end def string; gets.to_s.chomp end def rep(n, &b); Array.new(n, &b) end def yes; puts YESNO[1] end def no; puts YESNO[0] end def yesno t; puts YESNO[t] end def zip(xs, *yss); Enumerator.new { |y| xs.zip(*yss) { |a| y.yield(*a) } } end def max(*xs, &block); block_given? ? xs.max_by(&block) : xs.max end def min(*xs, &block); block_given? ? xs.min_by(&block) : xs.min end def minmax(*xs, &block); block_given? ? xs.minmax_by(&block) : xs.minmax end def gcd(*xs); xs.inject(0, :gcd) end def matrix(h, w, fill=nil, &block); return Array.new(h) { Array.new(w, &block) } if block_given?; Array.new(h) { [fill] * w } end def debug(x = nil); STDERR.puts (block_given? ? yield(x) : x).inspect if DEBUG; x end def debug_grid(grid, width = 1); grid.each { |row| STDERR.puts row.map { |x| x.inspect.ljust(width) }.join("") } if DEBUG; grid end def if_debug; yield if DEBUG end module Boolean def coerce(other); [other, to_i] end def +@; to_i end def to_int; to_i end def *(other); to_i * other end end class TrueClass include Boolean def to_i; 1 end end class FalseClass include Boolean def to_i; 0 end end class Integer def div_ceil(y); (self + y - 1) / y end def mod_inv(mod = MOD); pow(mod-2, mod) end def mod_div(y, mod = MOD); self * mod_inv(y, mod) % mod end def factorial(mod = MOD); (2..self).inject(1) { |f, x| f * x % mod } end def popcount; x = self; c = 0; while x > 0; c += 1 if x & 1 == 1; x >>= 1 end; c end #TODO: faster def bitbrute(&block); (1< 1; if yield((wj = (ac + wa) / 2)); ac = wj else wa = wj end; end; yield(ac) ? ac : nil end def lower_bound; ac, wa = self.end_open, self.begin; while ac - wa > 1; if yield((wj = (ac + wa) / 2)); ac = wj else wa = wj end; end; yield(ac) ? ac : nil end def shakutori(r2, &pred); Enumerator.new { |y| j, r = r2.begin, r2.end_open; each { |i| j += 1 while j + 1 < r and pred[i, j+1]; y.yield(i, j) } }; end def widest(&block); Enumerator.new { |y| j, n = self.begin, self.end_open; each { |i| j += 1 while j < n and block[i, j]; y.yield(i, j) if block[i, j] } } end end class Array def power(&block); (0 ... 1 << size).each(&block) end def sorted_merge(other); a = []; i = j = 0; n, m = size, other.size; if j < m and other[j] < self[i]; a << other[j]; j += 1 else; a << self[i]; i += 1 end while i < n; a.push(*other[j..-1]) if j < m; a end def upper_bound; ac, wa = 0, size; while wa - ac > 1; if yield(self[(wj = (ac + wa) / 2)]); ac = wj else; wa = wj end; end; ac end def lower_bound; ac, wa = size, 0; while wa - ac > 1; if yield(self[(wj = (ac + wa) / 2)]); ac = wj else; wa = wj end; end; ac end def cum(*xs, &op); a = []; a << xs[0] if xs.size > 0; a << x = self[0]; (1...size).each { |i| a << x = op[x, self[i]] }; a end def cumdiff(range); self[range.end_open] - self[range.begin]; end end module Enumerable def sorted_uniq; x = nil; filter { |y| c = x === y; x = y; !c } end def cumsum; ys = [0]; each { |x| ys << x + ys[-1] }; ys end end class Factorial def initialize(max, mod) @mod = mod @fac = [1, 1] @fin = [1, 1] @inv = [nil, 1] (2 .. max).each do |i| @fac[i] = @fac[i - 1] * i % mod @inv[i] = mod - @inv[mod % i] * (mod / i) % mod @fin[i] = @fin[i - 1] * @inv[i] % mod end end def fact(n) @fac[n] end def comb(n, k) return 0 if n < k or n < 0 or k < 0 @fac[n] * @fin[k] % @mod * @fin[n - k] % @mod end end main[]