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 9*1 + 10*2 + 11*2 + 12*2 = 75.
import math


number_of_tests = int(raw_input())

modulus = long(1000000007)

for x in xrange(number_of_tests):
    left, right = map(int, raw_input().split())
    
    result = 0
    bottom = left

    while bottom <= right:
        if bottom > 0:
            length_of_bottom = int(math.log10(bottom)) + 1
        elif bottom == 0:
            length_of_bottom = 1
        else:
            length_of_bottom = int(math.log10(-bottom)) + 2
        top = min((10 ** length_of_bottom) - 1, right)
        result = result + (bottom + top) * length_of_bottom * (top - bottom + 1) / 2
        bottom = top + 1

    print result % modulus