#!/usr/bin/ruby

# solves A = x + B^x   (uint32_t, no overflows)

a = Integer(ARGV.shift)
b = Integer(ARGV.shift)

def solve(a, b)
	x = 0
	carry = 0

	# per bit truth table, c = carry
	# c A B  x c
	# 0 0 0  0 0
	# 0 1 0  0 1
	# 1 0 0  1 0
	# 1 1 0  1 1
	# 0 1 1  0 0
	# 1 0 1  0 1
	# 0 1 1  1 0
	# 1 0 1  1 1

	# reordered
	# c A B  x c
	# 0 0 0  0 0
	# 0 1 0  0 1
	# 0 1 1  1 0
	# 0 1 1  0 0
	# 1 0 0  1 0
	# 1 0 1  0 1
	# 1 0 1  1 1
	# 1 1 0  1 1

	bit = lambda { |var, off| (var >> off) & 1 }

	31.downto(0) { |i|
		case [carry, bit[a, i], bit[b, i]]
		when [0, 0, 0]
			#x |= 1 << i
			carry = 0
		when [0, 0, 1]
			raise
		when [0, 1, 0]
			#x |= 1 << i
			carry = 1
		when [0, 1, 1]
			puts 'rand'
			x |= 1 << i if rand(2) == 0
			carry = 0
		when [1, 0, 0]
			x |= 1 << i
			carry = 0
		when [1, 0, 1]
			puts 'rand'
			x |= 1 << i if rand(2) == 0
			carry = 1
		when [1, 1, 0]
			x |= 1 << i
			carry = 1
		when [1, 1, 1]
			raise
		end
	}
	raise if carry == 1
	
	x
rescue
	abort "no solution for #{a} = x + #{b}^x"
end

x = solve(a, b)

puts "#{a} = x + #{b}^x <= x=#{x}"