Four digit Armstrong numbers

Four digit number is called Armstrong number if the sum of fourth power of its digits equals to the number. For example, 8208 = 8^4 + 2^4 + 0^4 + 8^4 is an Armstrong number. Print all Armstrong numbers from a to b.

Input

Two integers a and b (1000 ≤ a ≤ b ≤ 9999).

Output

Print in one line all Armstrong numbers from a to b.

Examples