Problem Description

In the ION Contest, there are a total of $n$ problems. The full score for each problem is $100$ points.

Problem $i$ has $a_i$ test points, and all test points in this problem have the same value, so $a_i$ must be a divisor of $100$. For each test point you pass, you will get the score equal to the value of that test point.

By some technical means, you learned that this year's Au cutoff score in the ION Contest is $t$ points.

Now, in problem $i$, you have already passed $b_i$ test points. As a strategic contestant, you want to know: for any $1\le j\le n$, if you spend all the remaining contest time grinding only problem $j$ (and do no other problems), what is the minimum number of additional test points you need to pass to get Au, that is, to make your total score $\ge t$.

Of course, you may be unable to turn the tables (get Au) by grinding a certain problem. In that case, you need to output NaN.

Input Format

Read input from standard input.

The first line contains a positive integer $n$, representing the total number of problems.

The next $n$ lines each contain two non-negative integers $a_i, b_i$, representing the number of test points in problem $i$ and the number of test points you have already passed. It is guaranteed that $a_i$ is a divisor of $100$ and $b_i \le a_i$.

The last line contains an integer $t$, representing the Au cutoff score.

Output Format

Write output to standard output.

If your score has already reached the Au cutoff, output one line with the string Already Au..

Otherwise, output $n$ lines. In line $i$, output one of the following two formats:

• A positive integer $c_i$, meaning the minimum number of additional test points you need to pass in problem $i$ to get Au.
• The string NaN, meaning you cannot turn the tables (get Au) through this problem.

7
100 100
20 20
25 23
25 10
20 14
25 11
20 0
447

NaN
NaN
1
1
1
1
1

7
100 100
20 20
25 23
25 10
20 14
25 11
20 0
446

Already Au.

7
100 100
20 20
20 10
25 13
20 20
25 16
20 6
509

NaN
NaN
3
4
NaN
4
3

7
100 100
20 19
20 20
25 11
20 20
25 25
20 6
509

Already Au.

Hint

[Sample Explanation #1]

It is easy to see that the current score is $100+100+92+40+70+44=446$, and the cutoff score is $447$. Therefore, in any problem where you have not gotten full marks, passing one more test point is enough.

[Constraints]

For all testdata, it is guaranteed that: $1\leq n\leq 7$, $0\leq b_i\leq a_i$, $1\leq a_i\leq 100$ and $a_i$ is a divisor of $100$, $0\leq t\leq 100n$.

Translated by ChatGPT 5