E. Insane Problem
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Wave 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 $$$\frac{y}{x} = k^n$$$.
Input

The 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 $$$r_2$$$ ($$$2 \leq k \leq 10^9, 1 \leq l_1 \leq r_1 \leq 10^9, 1 \leq l_2 \leq r_2 \leq 10^9$$$).

Output

For each test case, output the number of matching ordered pairs $$$(x, y)$$$ on a new line.

Example
Input
5
2 2 6 2 12
2 1 1000000000 1 1000000000
3 5 7 15 63
1000000000 1 5 6 1000000000
15 17 78 2596 20914861
Output
12
1999999987
6
1
197
Note

In 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 $$$(1,1\,000\,000\,000)$$$