Johann Carl Friedrich Gauß (1777 – 1855) was one of the most important German mathematicians. For those of you who remember the Deutsche Mark, a picture of him was printed on the 10 – DM bill. In elementary school, his teacher J. G. Büttner tried to occupy the pupils by making them add up the integers from 1 to 100. The young Gauß surprised everybody by producing the correct answers (5050) within seconds.

Can you write a computer program that can compute such sums really quickly?

Given two integers n and m, you should compute the sum of all the integers from n to m. In other words, you should compute

The first line contains the number of scenarios. Each scenario consists of a line containing the numbers n and m (−10⁹ ≤ n ≤ m ≤ 10⁹).

The output for every scenario begins with a line containing “Scenario #i:”, where i is the number of the scenario starting at 1. Then print the sum of all integers from n to m. Terminate the output for the scenario with a blank line.

#include 
    
     #include 
     
      #include 
      
       int main(void){    int ii, casenum;    __int64 n, m, i;    __int64 sum;    scanf("%d", &casenum);    for (ii = 1; ii <= casenum; ii++){        scanf("%I64d%I64d", &n, &m);        if (n > m){            i = m;            m = n;            n = i;        }        sum = (n + m) * (m - n + 1) / 2;        printf("Scenario #%d:\n%I64d\n\n", ii, sum);    }    return 0;}