Distributing Ballot Boxes

Today, besides SWERC'11, another important event is taking place in Spain that rivals it in importance: the General Elections. Every resident of the country aged 18 or over is asked to vote in order to choose representatives for the Congress of Deputies and the Senate. Do not worry that all the judges will suddenly abandon their supervising duties: voting is not compulsory.

The administration has a number of ballot boxes left over from past elections. Unfortunately, the person in charge of distributing the boxes among the cities was dismissed a few months ago due to budget cuts. As a consequence, the current assignment of boxes to cities, and of the people who must vote in each of them, is arguably far from optimal. Your task is to show how efficiently this could have been done.

The only rule when assigning ballot boxes to cities is that every city must receive at least one box. Each person votes in the box to which they have been assigned. Your goal is to find a distribution that minimizes the maximum number of people assigned to vote in a single box.

In the first sample case, two boxes go to the first city and the rest to the second, and exactly 100000 people are assigned to each of the (huge!) boxes in the most efficient distribution. In the second sample case, the cities receive 1, 2, 2, and 1 ballot boxes, and 1700 people from the third city are called to vote in each of that city's two boxes, making them the most crowded boxes of all in the optimal assignment.

The input consists of several test cases. The first line of each test case contains two integers $N$ ($1 \le N \le 500000$), the number of cities, and $B$ ($N \le B \le 2000000$), the number of ballot boxes. Each of the following $N$ lines contains an integer $a_i$ ($1 \le a_i \le 5000000$), the population of the $i$-th city.

A single blank line follows each test case. The last line of the input contains -1 -1 and must not be processed.

For each test case, output a single integer: the maximum number of people assigned to one box in the most efficient assignment.