Boltu and Balti are two friends. Boltu is a great programmer whereas Balti is a newbie programmer. But Balti thinks that he is also a great programmer, but Boltu can't accept Balti as a great programmer. Now Boltu challenges Balti to solve a task to prove himself as a great programmer. Balti accepts that challenge.

The task is Boltu will give him any 2 numbers N and M , he (Balti) has to find the sum of all numbers in the range N and M (inclusive). Balti knows that the equation of finding sum from 1 to n is $n(n+1)/2$.

Balti is getting stuck to find it from N to M. Now he wants your help. Help him to win this challenge by solving this problem.

Input

Each line of input contains two integers N and M (0 ≤ N,M ≤ 109). The numbers are separated by exactly one space. The end of file will indicate the end of input.

Output

You have to find the sum of numbers between N and M and print it as follows:

Sum of X to Y is: Z;

Here X is the smaller number, Y is the larger number and Z is the sum of all numbers between N and M (inclusive).

Sample

Input

Output

2 6
3 7

Sum of 2 to 6 is -> 20;
Sum of 3 to 7 is -> 25;

In the first sample test case the sum of numbers from 2 to 6 is $2+3+4+5+6 = 20$.

In the second sample test case the sum of numbers from 3 to 7 is $3+4+5+6+7 = 25$.