CF105B.Dark Assembly

Dark Assembly is a governing body in the Netherworld. Here sit the senators who take the most important decisions for the player. For example, to expand the range of the shop or to improve certain characteristics of the character the Dark Assembly's approval is needed.

The Dark Assembly consists of n senators. Each of them is characterized by his level and loyalty to the player. The level is a positive integer which reflects a senator's strength. Loyalty is the probability of a positive decision in the voting, which is measured as a percentage with precision of up to 10%.

Senators make decisions by voting. Each of them makes a positive or negative decision in accordance with their loyalty. If strictly more than half of the senators take a positive decision, the player's proposal is approved.

If the player's proposal is not approved after the voting, then the player may appeal against the decision of the Dark Assembly. To do that, player needs to kill all the senators that voted against (there's nothing wrong in killing senators, they will resurrect later and will treat the player even worse). The probability that a player will be able to kill a certain group of senators is equal to A / (A + B), where A is the sum of levels of all player's characters and B is the sum of levels of all senators in this group. If the player kills all undesired senators, then his proposal is approved.

Senators are very fond of sweets. They can be bribed by giving them candies. For each received candy a senator increases his loyalty to the player by 10%. It's worth to mention that loyalty cannot exceed 100%. The player can take no more than k sweets to the courtroom. Candies should be given to the senators before the start of voting.

Determine the probability that the Dark Assembly approves the player's proposal if the candies are distributed among the senators in the optimal way.

黑暗议会是魔界的一个管理机构。议会中坐着一群参议员，他们负责为玩家做出最重要的决策。例如，若要扩展商店的经营范围，或提升角色的某些属性，都需要获得黑暗议会的批准。

黑暗议会由 $n$ 名参议员组成。每名参议员均具有一个等级（level）和对玩家的忠诚度（loyalty）。等级是一个正整数，反映该参议员的实力；忠诚度则表示其在投票中投赞成票的概率，以百分比形式给出，精度可达 10%（即仅取 0%, 10%, 20%, …, 100% 中的值）。

参议员们通过投票作出决策：每位参议员依据其忠诚度独立地以对应概率投赞成票，否则投反对票。若投赞成票的参议员人数严格超过半数，则玩家的提案获得通过。

若投票后玩家的提案未获通过，则玩家可就黑暗议会的决议提出上诉。为此，玩家需击杀所有投反对票的参议员（击杀参议员并无不妥——他们之后会复活，但会对玩家更加敌视）。玩家成功击杀某一组参议员的概率为 $\frac{A}{A + B}$，其中 $A$ 是玩家所有角色等级之和，$B$ 是该组参议员等级之和。若玩家成功击杀全部投反对票的参议员，则其提案视为获得通过。

参议员们非常喜爱糖果。玩家可通过赠送糖果来贿赂他们：每赠送一颗糖果，一名参议员对玩家的忠诚度便提高 10%（注意：忠诚度上限为 100%，不可超过）。玩家最多可携带 $k$ 颗糖果进入法庭，且糖果必须在投票开始前分发给参议员。

请确定：在糖果以最优方式分配给参议员的前提下，黑暗议会最终批准玩家提案的概率。

The first line contains three integers n, k and A (1 ≤ n, k ≤ 8, 1 ≤ A ≤ 9999).

Then n lines follow. The i-th of them contains two numbers — b__i and l__i — the i-th senator's level and his loyalty.

The levels of all senators are integers in range from 1 to 9999 (inclusive). The loyalties of all senators are integers in range from 0 to 100 (inclusive) and all of them are divisible by 10.

第一行包含三个整数 $n$、$k$ 和 $A$（$1 \leq n, k \leq 8$，$1 \leq A \leq 9999$）。

接下来是 $n$ 行。其中第 $i$ 行包含两个数 —— $b_i$ 和 $l_i$，分别表示第 $i$ 位参议员的等级及其忠诚度。

所有参议员的等级均为 $1$ 到 $9999$（含端点）范围内的整数；所有参议员的忠诚度均为 $0$ 到 $100$（含端点）范围内的整数，且均能被 $10$ 整除。

Print one real number with precision 10 - 6 — the maximal possible probability that the Dark Assembly approves the player's proposal for the best possible distribution of candies among the senators.

输出一个实数，精度为 $10^{-6}$——即在对参议员分配糖果的最优方案下，黑暗议会批准玩家提案的最大可能概率。

In the first sample the best way of candies' distribution is giving them to first three of the senators. It ensures most of votes.

It the second sample player should give all three candies to the fifth senator.

在第一个样例中，糖果的最佳分配方式是将它们全部分给前三位参议员。这能确保获得最多的选票。

在第二个样例中，玩家应将全部三颗糖果都给予第五位参议员。