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Problem Q
Digit Sum
For a pair of integers $a$ and $b$, the digit sum of the interval $[a, b]$ is defined as the sum of all digits occurring in all numbers between (and including) $a$ and $b$. For example, the digit sum of $[28,31]$ can be calculated as:
\[ 2\! +\! 8 \; +\; 2\! +\! 9 \; +\; 3\! +\! 0 \; +\; 3\! +\! 1 = 28 \]Given the numbers $a$ and $b$, calculate the digit sum of $[a, b]$.
Input
On the first line one positive number: the number of test cases, at most 100. After that per test case:
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one line with two space-separated integers, $a$ and $b$ $(0 \le a \le b \le 10^{15})$.
Output
Per test case:
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one line with an integer: the digit sum of $[a, b]$.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 0 10 28 31 1234 56789 |
46 28 1128600 |
