Random Digital Exponentiation

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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 $b = 2^7 \cdot 10^2 + 4^4 \cdot 10 + 3^3 = 15\, 387$.

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

Input

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

Output

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.

Sample Input 1 Sample Output 1
243 15387
7 4 3