Kaleidoscopic Palindromes

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Nicholas Neverson was a student at Northlings Neverland Academy. As with any daydreaming student, Nicholas was playing around with a Kaleidoscope one day instead of paying attention to the teacher. Since this was math class, his daydreams quickly turned to palindromic numbers. A palindromic number is any number which reads the same forwards and backwards.

He describes his vision to you at lunch: numbers which are palindromic in several bases at once. Nicholas wonders how many such numbers exist. You decide you can quickly code up a program that given a range and a number $k$, outputs the number of numbers palindromic in all bases $j$, $2 \leq j \leq k$, in that range.

Input consists of three space-separated integers: $a$, $b$, and $k$. The input satisfies the following constraints:

\[ 0 \leq a \leq b \leq 2\, 000\, 000, \\ 2 \leq k \leq 100\, 000. \]Output the quantity of numbers between $a$ and $b$ inclusive which are palindromes in every base $j$, for $2 \leq j \leq k$.

Sample Input 1 | Sample Output 1 |
---|---|

1 356 2 |
36 |

Sample Input 2 | Sample Output 2 |
---|---|

18 118 13 |
0 |