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Walking Race
Time Limit:10000MS  Memory Limit:131072K
Total Submit:386 Accepted:80
Case Time Limit:3000MS

Description

flymouse¡¯s sister wc is very capable at sports and her favorite event is walking race. Chasing after the championship in an important competition, she comes to a training center to attend a training course. The center has N check-points numbered 1 through N. Some pairs of check-points are directly connected by two-way paths. The check-points and the paths form exactly a tree-like structure. The course lasts N days. On the i-th day, wc picks check-point i as the starting point and chooses another check-point as the finishing point and walks along the only simple path between the two points for the day¡¯s training. Her choice of finishing point will make it that the resulting path will be the longest among those of all possible choices.

After every day¡¯s training, flymouse will do a physical examination from which data will obtained and analyzed to help wc¡¯s future training be better instructed. In order to make the results reliable, flymouse is not using data all from N days for analysis. flymouse¡¯s model for analysis requires data from a series of consecutive days during which the difference between the longest and the shortest distances wc walks cannot exceed a bound M. The longer the series is, the more accurate the results are. flymouse wants to know the number of days in such a longest series. Can you do the job for him?

Input

The input contains a single test case. The test case starts with a line containing the integers N (N ¡Ü 106) and M (M < 109). Then follow N − 1 lines, each containing two integers fi and di (i = 1, 2, ¡­, N − 1), meaning the check-points i + 1 and fi are connected by a path of length di.

Output

Output one line with only the desired number of days in the longest series.

Sample Input

3 2
1 1
1 3

Sample Output

3

Hint

Explanation for the sample:

There are three check-points. Two paths of lengths 1 and 3 connect check-points 2 and 3 to check-point 1. The three paths along with wc walks are 1-3, 2-1-3 and 3-1-2. And their lengths are 3, 4 and 4. Therefore data from all three days can be used for analysis.

Source
POJ Monthly--2006.12.31, flymouse

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