Problem:
Score : 100 points

Problem Statement

We have N+M balls, each of which has an integer written on it.

It is known that:

The numbers written on N of the balls are even.

The numbers written on M of the balls are odd.

Find the number of ways to choose two of the N+M balls (disregarding order) so that the sum of the numbers written on them is even.

It can be shown that this count does not depend on the actual values written on the balls.

Constraints

0 \leq N,M \leq 100

2 \leq N+M

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the answer.

Sample Input 1

2 1

Sample Output 1

1

For example, let us assume that the numbers written on the three balls are 1,2,4.

If we choose the two balls with 1 and 2, the sum is odd;

If we choose the two balls with 1 and 4, the sum is odd;

If we choose the two balls with 2 and 4, the sum is even.

Thus, the answer is 1.

Sample Input 2

4 3

Sample Output 2

9

Sample Input 3

1 1

Sample Output 3

0

Sample Input 4

13 3

Sample Output 4

81

Sample Input 5

0 3

Sample Output 5

3

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

def gi() gets.to_i end
def gs() gets.chomp end
def gim() gets.split.map(&:to_i) end
def gsm() gets.split.map(&:chomp) end
def YesNo1(bool, yes="Yes", no="No") puts (bool ? yes : no) end
def YESNO2(bool, yes="YES", no="NO") puts (bool ? yes : no) end
def sqrt(i) i ** (1.0/2) end

def comb(n,k)
  return 0 if k > n
  result = 1
  1.upto(k) do |d|
    result *= n
    result /= d
    n -= 1
  end
  result
end

require "bigdecimal"
#####
n = gi
nums = gim
countDic = {}
nums.each do |num|
  if countDic[num] != nil
    countDic[num] = countDic[num] + 1
  else
    countDic[num] = 1
  end
end
#print countDic

combDic = {}
countDic.each do |k,v|
  combDic[k] = comb(v,2)
end
#print combDic

resDic = {}
combDic.each do |k,v|
  otherSum = combDic.reject {|key| key == k}.values.inject(:+)
  otherSum = 0 if otherSum == nil
  resDic[k] = otherSum + comb(countDic[k]-1,2)
end
#print resDic

nums.each do |num|
  puts resDic[num]
end