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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

module Main where

import           Debug.Trace
import qualified Data.Vector.Unboxed           as VU
import           Data.List
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char
import           Data.Maybe


getVUIntFromInputLineAtBSC8 :: IO (VU.Vector Int)
getVUIntFromInputLineAtBSC8 =
    VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine
getListIntFromInputLineAtBSC8 =
    unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine
readInt = fst . fromJust . BSC8.readInt
readIntList = map readInt . BSC8.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine

main :: IO ()
main = do
    [aM,aN] <- getListIntFromInputLineAtBSC8
    --aP                   <- getVUIntFromInputLineAtBSC8
    --aQ                   <- getVUIntFromInputLineAtBSC8
    --aR                   <- getVUIntFromInputLineAtBSC8

    --vP <- VU.fromList . take aX . reverse . sort <$> getIntList
    --vQ <- VU.fromList . take aY . reverse . sort <$> getIntList
    --vR <- VU.fromList . take (aX + aY) . reverse . sort <$> getIntList

    let combi = aM*(aM-1) `div` 2 + aN*(aN-1) `div` 2
    print combi