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ZOJ Problem Set - 4125
Sekiro

Time Limit: 1 Second      Memory Limit: 65536 KB

Sekiro: Shadows Die Twice is an action-adventure video game developed by FromSoftware and published by Activision. In the game, the players act as a Sengoku period shinobi known as Wolf as he attempts to take revenge on a samurai clan who attacked him and kidnapped his lord.

As a game directed by Hidetaka Miyazaki, Sekiro (unsurprisingly) features a very harsh death punishment. If the player dies when carrying $g$ amount of money, the amount of money will be reduced to $\left\lceil \frac{g}{2} \right\rceil$, where $\left\lceil \frac{g}{2} \right\rceil$ indicates the smallest integer $g'$ that $2g' \ge g$.

As a noobie of the game, BaoBao has died $k$ times in the game continuously. Given that BaoBao carried $n$ amount of money before his first death, and that BaoBao didn't collect or spend any money during these $k$ deaths, what's the amount of money left after his $k$ deaths?

Input

There are multiple test cases. The first line of the input contains an integer $T$ (about $10^3$), indicating the number of test cases. For each test case:

The first and only line contains two integers $n$ and $k$ ($0 \le n \le 10^9$, $1 \le k \le 10^9$), indicating the initial amount of money BaoBao carries and the number of times BaoBao dies in the game.

Output

For each test case output one line containing one integer, indicating the amount of money left after $k$ deaths.

Sample Input

4
10 1
7 1
10 2
7 2

Sample Output

5
4
3
2

Hint

For the third sample test case, when BaoBao dies for the first time, the money he carries will be reduced from 10 to 5; When he dies for the second time, the money he carries will be reduced from 5 to 3.


Author: WENG, Caizhi
Source: The 10th Shandong Provincial Collegiate Programming Contest
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