86 lines
2.3 KiB
Markdown
86 lines
2.3 KiB
Markdown
# A. Set
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[Codeforces](https://codeforces.com/contest/2029/problem/A)
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You are given a positive integer `k` and a set `S` of all integers from `l` to `r` (inclusive).
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You can perform the following two-step operation any number of times (possibly zero):
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First, choose a number `x` from the set `S`, such that there are at least `k` multiples of `x` in `S`
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(including `x` itself);
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Then, remove `x` from `S` (note that nothing else is removed).
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Find the maximum possible number of operations that can be performed.
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## Input
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Each test contains multiple test cases. The first line of the input contains a single integer `t`
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(1 ≤ `t` ≤ 104) — the number of test cases. The description of test cases follows.
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The only line of each test case contains three integers `l`, `r`, and `k` (1 ≤ `l` ≤ `r` ≤ 109, 1 ≤ `k` ≤ `r` − `l` + 1) — the minimum integer in `S`, the maximum integer in `S`, and the parameter `k`.
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## Output
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For each test case, output a single integer — the maximum possible number of operations that can be performed.
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## Example
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Input
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```
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8
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3 9 2
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4 9 1
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7 9 2
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2 10 2
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154 220 2
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147 294 2
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998 24435 3
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1 1000000000 2
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```
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Output
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```
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2
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6
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0
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4
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0
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1
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7148
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500000000
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```
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## Note
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In the first test case, initially, S={3,4,5,6,7,8,9}.
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One possible optimal sequence of operations is:
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- Choose x=4 for the first operation, since there are two multiples of 4 in S: 4 and 8. S becomes equal to {3,5,6,7,8,9};
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- Choose x=3 for the second operation, since there are three multiples of 3 in S: 3, 6, and 9. S becomes equal to {5,6,7,8,9}.
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In the second test case, initially, S={4,5,6,7,8,9}. One possible optimal sequence of operations is:
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- Choose x=5, S becomes equal to {4,6,7,8,9};
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- Choose x=6, S becomes equal to {4,7,8,9};
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- Choose x=4, S becomes equal to {7,8,9};
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- Choose x=8, S becomes equal to {7,9};
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- Choose x=7, S becomes equal to {9};
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- Choose x=9, S becomes equal to {}.
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In the third test case, initially, S={7,8,9}. For each x in S, no multiple of x other than x itself can be found in S.
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Since k=2, you can perform no operations.
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In the fourth test case, initially, S={2,3,4,5,6,7,8,9,10}. One possible optimal sequence of operations is:
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- Choose x=2, S becomes equal to {3,4,5,6,7,8,9,10};
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- Choose x=4, S becomes equal to {3,5,6,7,8,9,10};
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- Choose x=3, S becomes equal to {5,6,7,8,9,10};
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- Choose x=5, S becomes equal to {6,7,8,9,10}.
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