## USACO 2012 December Contest, Gold

## Problem 3. Running Away From the Barn

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Problem 3: Running Away From the Barn [Richard Peng, 2012]
It's milking time at Farmer John's farm, but the cows have all run away!
Farmer John needs to round them all up, and needs your help in the search.
FJ's farm is a series of N (1 <= N <= 200,000) pastures numbered 1...N
connected by N - 1 bidirectional paths. The barn is located at pasture
1, and it is possible to reach any pasture from the barn.
FJ's cows were in their pastures this morning, but who knows where
they ran to by now. FJ does know that the cows only run away from the
barn, and they are too lazy to run a distance of more than L. For
every pasture, FJ wants to know how many different pastures cows
starting in that pasture could have ended up in.
Note: 64-bit integers (int64 in Pascal, long long in C/C++ and long in
Java) are needed to store the distance values.
PROBLEM NAME: runaway
INPUT FORMAT:
* Line 1: 2 integers, N and L (1 <= N <= 200,000, 1 <= L <= 10^18)
* Lines 2..N: The ith line contains two integers p_i and l_i. p_i (1
<= p_i < i) is the first pasture on the shortest path between
pasture i and the barn, and l_i (1 <= l_i <= 10^12) is the
length of that path.
SAMPLE INPUT (file runaway.in):
4 5
1 4
2 3
1 5
OUTPUT FORMAT:
* Lines 1..N: One number per line, the number on line i is the number
pastures that can be reached from pasture i by taking roads
that lead strictly farther away from the barn (pasture 1)
whose total length does not exceed L.
SAMPLE OUTPUT (file runaway.out):
3
2
1
1
OUTPUT DETAILS:
Cows from pasture 1 can hide at pastures 1, 2, and 4.
Cows from pasture 2 can hide at pastures 2 and 3.
Pasture 3 and 4 are as far from the barn as possible, and the cows can hide
there.

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