For real parameters alpha >= 0 and beta > 1, consider the weight function

w(x) = x^alpha exp(-x^beta) on (0, infinity).

The n-point Gaussian quadrature rule for this weight is the unique choice of nodes x_1 < ... < x_n in (0, infinity) and positive weights w_1, ..., w_n such that

integral from 0 to infinity of f(x) w(x) dx = w_1 f(x_1) + ... + w_n f(x_n)

holds exactly for every polynomial f of degree at most 2n - 1.

Given alpha, beta and n, output the rule.

Input

One line with alpha, beta (each with at most 6 digits after the decimal point) and the integer n.

Output

n lines. Line i contains x_i and w_i, nodes in increasing order, each with absolute error at most 1e-10 or relative error at most 1e-7.

Constraints

0 <= alpha <= 5

1.1 <= beta <= 4

1 <= n <= 20

Scoring

This is a standard problem: a submission scores full points if it produces the correct output for every test case, and zero otherwise.

Numeric answers are accepted if they are within an absolute tolerance of 1e-10 or a relative tolerance of 1e-07 of the expected value.