Given a positive integer (call it $N$) and a position in that integer (call it $P$) transform $N$. To transform $N$, find the $P^{th}$ digit of $N$ from the right:

• Replace each of the digits to the left by the sum of that digit and the $P^{th}$ digit.
• Replace each of the digits to the right by the absolute value of the difference between it and the $P^{th}$ digit.
• Replace the $P^{th}$ digit by the number of different prime factors of $N$. Note that $1$ is not a prime number, and it has no prime factors. A prime number has exactly one prime factor (namely, itself).

INPUT FORMAT

There will be $5$ sets of data. Each set contains two positive integers: $N$ and $P$. $N$ will be less than $1015$, and $P$ will be valid.

OUTPUT FORMAT

The transformed value of each input set. The printed number may not have any spaces between the digits.

SAMPLE

INPUT

102438 3
4329 1
6710 2
16807 1
60098065452 7

OUTPUT

546414
1312113
7841
8131571
1488173823436