题目描述

Define the ''digit product'' $f(x)$ of a positive integer $x$ as the product of all its digits. For example, $f(1234) = 1 \times 2 \times 3 \times 4 = 24$, and $f(100) = 1 \times 0 \times 0 = 0$.

Given two integers $l$ and $r$, please calculate the following value:

$$(\prod_{i=l}^r f(i)) \mod (10^9+7)$$

In case that you don't know what $\prod$ represents, the above expression is the same as

$$(f(l) \times f(l+1) \times \dots \times f(r)) \mod (10^9+7) $$

输入格式

There are multiple test cases. The first line of the input contains an integer $T$ (about $10^5$), indicating the number of test cases. For each test case:

The first and only line contains two integers $l$ and $r$ ($1 \le l \le r \le 10^9$), indicating the given two integers. The integers are given without leading zeros.

输出格式

For each test case output one line containing one integer indicating the answer.

2
1 9
97 99

362880
367416

提示

For the first sample test case, the answer is $9! \mod (10^9+7) = 362880$.

For the second sample test case, the answer is $(f(97) \times f(98) \times f(99)) \mod (10^9+7) = (9 \times 7 \times 9 \times 8 \times 9 \times 9) \mod (10^9+7) = 367416$.