#P1562A. The Miracle and the Sleeper
The Miracle and the Sleeper
Description
You are given two integers $l$ and $r$, $l\le r$. Find the largest possible value of $a \bmod b$ over all pairs $(a, b)$ of integers for which $r\ge a \ge b \ge l$.
As a reminder, $a \bmod b$ is a remainder we get when dividing $a$ by $b$. For example, $26 \bmod 8 = 2$.
Each test contains multiple test cases.
The first line contains one positive integer $t$ $(1\le t\le 10^4)$, denoting the number of test cases. Description of the test cases follows.
The only line of each test case contains two integers $l$, $r$ ($1\le l \le r \le 10^9$).
For every test case, output the largest possible value of $a \bmod b$ over all pairs $(a, b)$ of integers for which $r\ge a \ge b \ge l$.
Input
Each test contains multiple test cases.
The first line contains one positive integer $t$ $(1\le t\le 10^4)$, denoting the number of test cases. Description of the test cases follows.
The only line of each test case contains two integers $l$, $r$ ($1\le l \le r \le 10^9$).
Output
For every test case, output the largest possible value of $a \bmod b$ over all pairs $(a, b)$ of integers for which $r\ge a \ge b \ge l$.
Samples
4
1 1
999999999 1000000000
8 26
1 999999999
0
1
12
499999999
Note
In the first test case, the only allowed pair is $(a, b) = (1, 1)$, for which $a \bmod b = 1 \bmod 1 = 0$.
In the second test case, the optimal choice is pair $(a, b) = (1000000000, 999999999)$, for which $a \bmod b = 1$.