CF747F Igor and Interesting Numbers

Igor likes hexadecimal notation and considers positive integer in the hexadecimal notation interesting if each digit and each letter in it appears no more than $ t $ times. For example, if $ t=3 $ , then integers 13a13322, aaa, abcdef0123456789 are interesting, but numbers aaaa, abababab and 1000000 are not interesting. Your task is to find the $ k $ -th smallest interesting for Igor integer in the hexadecimal notation. The integer should not contain leading zeros.

The first line contains the two integers $ k $ and $ t $ ( $ 1

Print in the hexadecimal notation the only integer that is the $ k $ -th smallest interesting integer for Igor.

The first 20 interesting integers if $ t=1 $ : 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, 10, 12, 13, 14, 15. So the answer for the first example equals 12.