3610：Maclaurin Series of Reciprocals

Any function f(x) that is infinitely differentiable in the neighborhood of the point x = 0 can be expanded into a Maclaurin series

__poj_jax_start__f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^2+\frac{f^{(3)}(0)}{3!}x^3+\cdots__poj_jax_end__,

or more compactly,

__poj_jax_start__\sum_{k=0}^{\infty}\frac{f^{(k)}(0)}{k!}x^k__poj_jax_end__.

Under certain conditions, f(x) is equal to its Maclaurin series for all x sufficiently close to 0.

Often, the Maclaurin series of f(x) is written up to only order x^n-1 with a Peano remainder term, i.e.,　

__poj_jax_start__\sum_{k=0}^{n-1}\frac{f^{(k)}(0)}{k!}x^k+\mathcal{O}(x^n)__poj_jax_end__,

which facilitates the evaluation of f(x). The series being truncated to the x^n-1 term, details about higher-order terms are inevitably lost. However, certain information concerning the series remains well-preserved. For instance, the Maclaurin series of 1/f(x) with an identical Peano remainder term can still be found.

Given the Maclaurin series of a function f(x) with a Peano remainder term, determine that of the reciprocal of f(x).

The input consists of a single test case.

The first line contains an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a fraction p_k/q_k (0 ≤ k ≤ n - 1) where p_k and q_k (-100 ≤ p_k ≤ 100, 1 ≤ q_k ≤ 100) are integers coprime to each other in the form either p_k/q_k (if qk ≠ 1) or p_k (if q_k = 1). It is guaranteed that p₀ ≠ 0.

The given numbers represent the Maclaurin series

__poj_jax_start__\sum_{k=0}^{n-1}\frac{p_k}{q_k}x^k+\mathcal{O}(x^n)__poj_jax_end__

of some function f(x).

Let the Maclaurin series of 1/f(x) be

__poj_jax_start__\sum_{k=0}^{n-1}\frac{p'_k}{q'_k}x^k+\mathcal{O}(x^n)__poj_jax_end__

where q_k' > 0, and p_k' and q_k' are integers coprime to each other. Output n lines each of the form either p_k'/q_k' (if q_k' ≠ 1) or p_k' (if q_k' = 1), listing the coefficients of 1, x, x², ... , x^n-1 in order.