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S. 46. Unlike most belief systems, Flagland's mythology is deeply interlaced with elements of natural sciences. They think for example that it brings misfortune if the main sail of a ship is not square-shaped, or its side length (in meters) is not a power of 2. According to this, only square-shaped sailcloths with side length of a power of 2 are sold in local harbors, and tailors only join up 4 sailcloths of the same size to produce a twice as big sail.

Create your program to calculate the minimal price of a sailcloth of required size, if prices of various available sailcloths are known.

The first line of the standard input contains three integers (separated by a space): the number of available sailcloths 1\le N\le
1\;000\;000 on the market, the side length 1\leA=2a\le2048 of the required sailcloth, and the sewing cost 0\leV\le1000 in (linear) meters. Then each of the following N lines contains two integers: the side lengths 1\leBi=2bi\leA of available sailcloths and their prices 1\le C_i \le 1\;000\;000\;000. Lines of the input are ordered monotonically first according to side lengths, then to prices.

The only line of the standard output should contain a single integer: the minimal price to make the required sailcloth. (This price consists of the cost of materials and possible sewing.) You can assume that a solution always exists.

In the figure, ``Bemenet'' is input, ``Kimenet'' is output, ``Optimális megoldás'' is the optimal solution, while ``szaggatott vonal jelöli a varrásokat'' is ``seams are denoted by dashed lines''.

The source code and project files of your solution (without the .exe file or any other auxiliary files generated by the compiler) together with a short documentation describing your solution should be submitted in a compressed folder (s46.zip).

Sample test cases: s46teszt.zip. Your solution has to give (a not neccessarily correct) answer to 5 out of 10 inputs in order to be judged.

(10 points)

Deadline expired on 12 October 2009.

Statistics on problem S. 46.
27 students sent a solution.
10 points:Berecz Dénes, Éles András, Mokcsay 026 Ádám, Várnai Péter.
9 points:Adrián Patrik, Bodosi Eszter, Fejér 267 László, Kovács 125 András, Nagy 111 Miklós, Nagy Róbert.
8 points:8 students.
7 points:4 students.
6 points:2 students.
5 points:1 student.
4 points:1 student.
3 points:1 student.

  • Problems in Information Technology of KöMaL, September 2009

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