E. Insane Problemtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputWave is given five integers $$$k$$$, $$$l_1$$$, $$$r_1$$$, $$$l_2$$$, and $$$r_2$$$. Wave wants you to help her count the number of ordered pairs $$$(x, y)$$$ such that all of the following are satisfied: $$$l_1 \leq x \leq r_1$$$. $$$l_2 \leq y \leq r_2$$$. There exists a non-negative integer $$$n$$$ such that $$$\frac{y}{x} = k^n$$$. InputThe first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases.The only line of each test case contains five integers $$$k$$$, $$$l_1$$$, $$$r_1$$$, $$$l_2$$$, and $$$r_2$$$ ($$$2 \leq k \leq 10^9, 1 \leq l_1 \leq r_1 \leq 10^9, 1 \leq l_2 \leq r_2 \leq 10^9$$$).OutputFor each test case, output the number of matching ordered pairs $$$(x, y)$$$ on a new line.ExampleInput52 2 6 2 122 1 1000000000 1 10000000003 5 7 15 631000000000 1 5 6 100000000015 17 78 2596 20914861Output12
1999999987
6
1
197
NoteIn the third test case, the matching ordered pairs are the following: $$$(5,15)$$$ $$$(5,45)$$$ $$$(6,18)$$$ $$$(6,54)$$$ $$$(7,21)$$$ $$$(7,63)$$$ In the fourth test case, the only valid ordered pair is $$$(1,1\,000\,000\,000)$$$