{"trustable":false,"sections":[{"title":"statement","value":{"format":"MD","content":"Undoubtedly you know of the Fibonacci numbers. Starting with\nF1 \u003d 1 and F2 \u003d 1, every next number is the sum of the two\nprevious ones. This results in the sequence 1, 1, 2, 3, 5, 8, 13, . . ..\nNow let us consider more generally sequences that obey the\nsame recursion relation\n\n$G_i \u003d G_{i−1} + G_{i−2}$ for $i \u003e 2$\n\nbut start with two numbers $G_1 ≤ G_2$ of our own choice. We shall call these Gabonacci sequences. For example, if one uses $G_1 \u003d 1$ and $G_2 \u003d 3$, one gets what are known as the Lucas numbers:\n1, 3, 4, 7, 11, 18, 29, . . .. These numbers are – apart from 1 and 3 – different from the Fibonacci numbers.\n\nBy choosing the first two numbers appropriately, you can get any number you like to appear in the Gabonacci sequence. For example, the number n appears in the sequence that starts with 1 and n − 1, but that is a bit lame. It would be more fun to start with numbers that are as small as possible, would you not agree?\n"}},{"title":"input","value":{"format":"MD","content":"On the first line one positive number: the number of test cases, at most 100. After that per test case:\n\n• one line with a single integer $n (2 ≤ n ≤ 10^9)$: the number to appear in the sequence.\n"}},{"title":"output","value":{"format":"MD","content":"Per test case:\n\n• one line with two integers a and b $(0 \u003c a ≤ b)$, such that, for $G_1 \u003d a$ and $G_2 \u003d b$,\nGk \u003d n for some k. These numbers should be the smallest possible, i.e., there should be\nno numbers $a_0$ and $b_0$ with the same property, for which $b_0 \u003c b\u0027$ or for which $b\u0027 \u003d b$ and $a\u0027 \u003c a$."}},{"title":"example-input","value":{"format":"MD","content":"```\n5\n89\n123\n1000\n1573655\n842831057\n```"}},{"title":"example-output","value":{"format":"MD","content":"```\n1 1\n1 3\n2 10\n985 1971\n2 7\n```"}}]}