Score : 900 points
Akaki, a patissier, can make N kinds of doughnut using only a certain powder called "Okashi no Moto" (literally "material of pastry", simply called Moto below) as ingredient. These doughnuts are called Doughnut 1, Doughnut 2, ..., Doughnut N. In order to make one Doughnut i (1 ≤ i ≤ N), she needs to consume m_i grams of Moto. She cannot make a non-integer number of doughnuts, such as 0.5 doughnuts.
The recipes of these doughnuts are developed by repeated modifications from the recipe of Doughnut 1. Specifically, the recipe of Doughnut i (2 ≤ i ≤ N) is a direct modification of the recipe of Doughnut p_i (1 ≤ p_i < i).
Now, she has X grams of Moto. She decides to make as many doughnuts as possible for a party tonight. However, since the tastes of the guests differ, she will obey the following condition:
At most how many doughnuts can be made here? She does not necessarily need to consume all of her Moto.
Input is given from Standard Input in the following format:
N X D m_1 m_2 p_2 : m_N p_N
Print the maximum number of doughnuts that can be made under the condition.
3 100 1 15 10 1 20 1
7
She has 100 grams of Moto, can make three kinds of doughnuts, and the conditions that must hold are c_1 ≤ c_2 ≤ c_1 + 1 and c_1 ≤ c_3 ≤ c_1 + 1. It is optimal to make two Doughnuts 1, three Doughnuts 2 and two Doughnuts 3.
3 100 10 15 10 1 20 1
10
The amount of Moto and the recipes of the doughnuts are not changed from Sample Input 1, but the last conditions are relaxed. In this case, it is optimal to make just ten Doughnuts 2. As seen here, she does not necessarily need to make all kinds of doughnuts.
5 1000000000 1000000 123 159 1 111 1 135 3 147 3
7496296