Random Digital Exponentiation

In a random digital exponentiation (RDE) cipher, each digit of a number $a$ is raised to a certain power which is determined by a randomly chosen encryption key. The encrypted number is the number that results when each digit is replaced with its power at the corresponding place value.

For instance, for $a = 243$ and an encryption key of 7 4 3, the encrypted value $b$ would be $b = 2^7 \times 10^2 + 4^4 \times 10 + 3^3 = 15\\,387$.

Given a plaintext value $a$ and an encrypted value $b$, find the encryption key that was used!

The input will contain a single test case containing two numbers $a$ and $b$ ($0 \le a \le b \le 2\\,147\\,483\\,647$).

Print the encryption key, which is the list of exponents to which each digit in $a$ was raised, separated by spaces, starting from the leftmost digit's exponent. Each exponent should be a natural number. You are guaranteed that the encryption key exists and is unique.