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## 1467. Sum of Degrees

Time limit: 1.0 second
Memory limit: 64 MB
On an exam:
— Find the sum of the k-th degrees of the first N positive integers.
— That's easy. What's N?
N is unknown, solve the problem in the general case.
— So how can I find this sum if N is unknown?
— We discussed it at the lectures. The sum 1k + 2k + 3k + … + Nk for any k is a polynomial P(N) of degree k+1 with rational coefficients. For example, 1 + … + N = N(N+1)/2. Given k, find the coefficients of this polynomial.
Can you solve this problem?

### Input

An integer 0 ≤ k ≤ 30.

### Output

Output coefficients of the polynomial P(N) = Ak+1Nk+1 + AkNk + … +A1N + A0 in the form of k+2 irreducible fractions. A fraction has the form "a/b" or "−a/b", where a and b are integers, b ≥ 1, a ≥ 0. The coefficients must be given in the order of descending degrees (from Ak+1 to A0). It is not allowed to omit denominators of the fractions or leave out zero coefficients. Separate the fractions with a space.

### Sample

inputoutput
`1`
`1/2 1/2 0/1`
Problem Author: Alexander Ipatov
Problem Source: Ural SU Contest. Petrozavodsk Winter Session, January 2006
Tags: none