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
1^{k} + 2^{k} + 3^{k} + … + *N*^{k}
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

### Output

Output coefficients of the polynomial
*P*(*N*) = *A*_{k+1}*N*^{k+1} + *A*_{k}N^{k} + …
+*A*_{1}*N* + *A*_{0}
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 *A*_{k+1} to *A*_{0}).
It is not allowed to omit denominators of the fractions
or leave out zero coefficients.
Separate the fractions with a space.

### Sample

**Problem Author: **Alexander Ipatov

**Problem Source: **Ural SU Contest. Petrozavodsk Winter Session, January 2006