 Contests Virtual Contests Problems Submit Runs Status Rank List Forum

2558.   Medium Size Summations (R2D2)
Time Limit: 5.0 Seconds   Memory Limit: 65536K
Total Runs: 123   Accepted Runs: 53

R2-D2 (our well known friendly robot) needs to perform some operations quickly to save his space ship. These operations require computing long summations and a division. Moreover, he needs to find the exact solution and he is required to present a report with the results. For that, he needs to simplify his solution as much as possible.

We assume that there is an array available (X1, X2 , ...) of 99999999 elements.

The array has the peculiar property that the average of the first K numbers is equal to the average of the index K and the number 1.

R2-D2 needs to do the following: Given a natural number N less than 99999999, his assignment is to compute the function:

F(N) = F1(N) / F2(N) where:

F1(N) = N × (Σ_{0 ≤ k ≤ N} k4/Xk)

F2(N) = (Σ_{0 ≤ k ≤ N} k3/Xk) × (Σ_{0 ≤ k ≤ N} k2/Xk )

That is, F1(N) = N × ( 1/X1 + 16/X2 + ... + N4/XN) and

F2(N) = ( 1/X1 + 8/X2 + ... + N3/XN) × ( 1/X1 +4/X2 + ... + N2/XN)

Since R2-D2 needs an exact solution, we ask him to report the following:
The solution needs to be given as a pair of relative prime numbers a,b such that f(N) = a/b if the solution is not an exact integer. Otherwise just give the exact integer. The numbers processed by R2-D2 were of eight digits (99999999). Remember that R2-D2 was built long long time ago. His circuits are not that fast but he is clever. R2-D2 was able to perform one of these operations in less than one second. Can you do this assignment as fast as R2-D2 did it?

### Input

You will receive an input line with natural numbers separated by comma. Each number is less than 99999999. You will receive no more than 20 numbers.

### Output

You need to give a sequence of lines each one with the solution of the corresponding input case. The solution is either a pair of natural numbers separated by the symbol / representing the pair a,b mentioned above (when the division is not exact) or just one natural number (when the division is exact). Notice that these numbers could require more than 8 digits.

### Sample Input

1,2


### Sample Output

1
6/5


Source: Mexico and Central America 2006
Submit   List    Runs   Forum   Statistics

Tianjin University Online Judge v1.3.0
Maintance:Fxz. Developer: SuperHacker, G.D.Retop, Fxz