A fat number is a number that the sum of its digits is equal with the multiple of its digits.

Example: 321 and 123 and 213 are fat number because 3 + 2 + 1 = 3 * 2 * 1.

Your mission is finding all fat number between a and b inclusive.

Input

The first line of the input consist of a single integer number t which determines the number of tests.

In each of next t lines there is two number a and b separated by a space.

Constraints

• 0 < t ≤ 1 000
• 0 ≤ a, b ≤ 10 000 000

Output

For each test case print out all fat number found inside the range which separated by a space.

Separate your answers with a new line character.

Example

Input:
2
8 15
2000 1

Output:
8 9
1 2 3 4 5 6 7 8 9 22 123 132 213 231 312 321 1124 1142 1214 1241 1412 1421