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134 - ZOJ Monthly, June 2014 - F
First Digit

Time Limit: 2 Seconds      Memory Limit: 65536 KB      Special Judge

Benford's Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, the number 1 occurs as the leading digit about 30% of the time, while larger numbers occur in that position less frequently: 9 as the first digit less than 5% of the time. Benford's Law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution.

This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.

A set of numbers is said to satisfy Benford's Law if the leading digit d ∈ {1, ..., 9} occurs with probability P(d) = log10(d + 1) - log10(d). Numerically, the leading digits have the following distribution in Benford's Law:

d 1 2 3 4 5 6 7 8 9
P(d) 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6%

Now your task is to predict the first digit of be, while b and e are two random integer generated by discrete uniform distribution in [1, 1000]. Your accuracy rate should be greater than or equal to 25% but less than 60%. This is not a school exam, and high accuracy rate makes you fail in this task. Good luck!

Input

There are multiple test cases. The first line of input contains an integer T (about 10000) indicating the number of test cases. For each test case:

There are two integers b and e (1 <= b, e <= 1000).

Output

For each test case, output the predicted first digit. Your accuracy rate should be greater than or equal to 25% but less than 60%.

Sample Input

20
206 774
133 931
420 238
398 872
277 137
717 399
820 754
997 463
77 791
295 345
375 501
102 666
95 172
462 893
509 839
20 315
418 71
644 498
508 459
358 767

Sample Output

8
2
2
1
4
2
1
2
1
1
4
6
2
4
9
7
2
7
1
7

Hint

The actual first digits of the sample are 8, 2, 2, 1, 4, 2, 1, 2, 1, 1, 3, 5, 1, 3, 8, 6, 1, 6, 9 and 6 respectively. The sample output gets the first 10 cases right, so it has an accuracy rate of 50%.

Reference

Benford's law in Wikipedia


Author: ZHOU, Yuchen
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