Polo, the Penguin, likes numbers. He says that the goodness of a number is itself multiplied by the number of digits in it's decimal representation. For example, the goodness of the integer 474 is 474*3 = 1422.
Help him to count the sum of goodness of all integers from L to R, inclusive. Since the answer can be too large, output it modulo 1,000,000,007 (10^9+7).

Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. The only line of each test case contains the pair of integers L and R, separated by a single space.

Output
For each test case, output a single line containing the answer to the corresponding test case.

Constraints

1 ≤ T ≤ 1,000
1 ≤ L ≤ R ≤ 1,000,000,000 (10^9)

Example
Input:
1
9 12

Output:
75

Explanation
Example case 1. The answer is 91 + 102 + 112 + 122 = 75.

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