Taking Medicine

Time limit1sMemory limit1024 MB

Summary

Decide whether three doses a day, each taken right after a meal within a fixed window, can keep the effect of K minutes active without a gap for N days.

Level: Medium5 of 10
Topics: Greedy, Math, Simulation
Solved: No attempts yet

Problem

Yugyeom caught a cold, and the hospital gave him medicine for $N$ days. Yugyeom hates being sick, so once he starts the cold medicine, he wants the effect to last without a gap until he has finished the whole course.

Yugyeom must take the medicine three times a day, right after meals, and the effect lasts $K$ minutes. He can eat three meals a day, each within a fixed time window. The time spent eating and taking the medicine is ignored. Determine whether you can arrange the three meal times on each day so that the effect does not lapse until the last dose on day $N$ is taken.

Input

The first line contains the number of days $N$ and the duration of the effect $K$ , separated by a space. $(1 \leq N \leq 100\,000; 1 \leq K \leq 1\,440)$

The second line contains $A_s,A_e,B_s,B_e,C_s,C_e$ separated by spaces, where $0 \leq A_s \leq A_e \lt B_s \leq B_e \lt C_s \leq C_e \lt 1\,440$ . Each pair gives the start and end, in minutes, of one of the three windows for meals. Day 1 runs from minute 0 to minute 1439, which is 1440 minutes in total.

All numbers in the input are integers.

Output

Print YES if the effect can last without a gap until the last dose on day $N$ is taken. Otherwise, print NO.

Examples3

Example 1
Input
```
10 480
360 360 840 840 1320 1320
```
Expected output
```
YES
```
Example 2
Input
```
3 480
360 360 820 820 1300 1300
```
Expected output
```
NO
```
Example 3
Input
```
2 476
360 380 840 860 1320 1340
```
Expected output
```
YES
```