## ETFD - Euler Totient Function Depth

Lucky is fond of Number theory, one day he was solving a problem related to Euler Totient Function (phi) and found an interesting property of phi : phi(1) = 1, and for x > 1: phi(x) < x.
So if we define a sequence with a0 = x, and for n > 0: an = phi(an-1), this sequence will be constant equal to 1 starting from some point. Lets define depth(x) as minimal n such that an = 1.
Now he is wondering how many numbers in a given range have depth equal to given number k. As you are a good programmer help Lucky with his task.

### Input

Your input will consist of a single integer T  followed by a newline and T test cases.
Each test cases consists of a single line containing integers m, n, and k.

### Output

Output for each test case one line containing the count of all numbers whose depth equals to k in given range [m, n].

### Constraints

```T < 10001
1 ≤ m ≤ n ≤ 10^6
0 ≤ k < 20
```

### Example

```Input:
5
1 3 1
1 10 2
1 10 3
1 100 3
1 1000000 17

Output:
1
3
5
8
287876```

Explanation ::suppose number is 5 ; its depth will be 3. ( 5 -> 4 -> 2 -> 1 )

Note ::Depth for 1 is 0.

 Added by: [Lakshman] Date: 2015-01-14 Time limit: 2s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 JS-MONKEY Resource: ETF