4124번 - Secret Polynomial 다국어

문제

You may have encountered IQ tests with inane questions such as the following: find the next number in the sequence 1, 2, 3, __. Obviously the correct answer is 16, since the sequence lists the values f(1), f(2), f(3), f(4), ..., where f(x) = 2x³ - 12x² + 23x - 12. More generally, given some information about the values of a polynomial, can you find the polynomial? We will restrict our attention to polynomials whose coefficients are all non-negative integers.

입력

The first line of input contains an integer 0 < n <= 10000, the number of polynomials to be identified. Each of the next n lines contains two integers, the values f(1) and f(f(1)), where f is the polynomial to be found. Each of these values fits within the range of a signed two's complement 32-bit integer.

출력

For each polynomial to be found, output a single line listing its coefficients separated by spaces. Assuming the degree of the polynomial is d, list the d+1 coefficients in descending order of power (i.e. starting with the coefficient of xd and finishing with the coefficient of x⁰). If the polynomial is the zero polynomial, just output 0. If no polynomial f has the desired values of f(1) and f(f(1)), instead output a line containing the word IMPOSSIBLE. If multiple polynomials f have the desired values of f(1) and f(f(1)), instead output a line containing the word AMBIGUOUS.

제한

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