Hayden traveled to France with his friend Matt and Sunny. They bought a long baguette with length $N$ units, which could be seen as lying on a number line from position $0$ to position $N$.

However, Matt and Sunny have terrible taste.

Matt loves wasabi. He spreads wasabi from position $A$ to position $B$.

Sunny loves peanut butter. He spreads peanut butter from position $C$ to position $D$.

Hayden hates both wasabi and peanut butter. He is very hungry and wants to eat a single continuous piece of baguette with neither wasabi nor peanut butter on it, with at least $K$ units. Determine whether Hayden can find such a piece.

Input

The first line contains two integers $N$ and $K$ ($1 \leq K \leq N \leq 10^9$).
The second line contains four integers $A, B, C, D$ ($0 \leq A \lt B \leq N$ and $0 \leq C \lt D \leq N$).

Output

Print "Yes" if Hayden can eat a single continuous piece of baguette with neither wasabi nor peanut butter on it with at least $K$ units.
Otherwise, print "No".

Subtasks

Subtask 1 (5 pts): $A = C$ and $B = D$.
Subtask 2 (10 pts): $A \lt C$ and $B \gt D$.
Subtask 3 (15 pts): $B \leq C$.
Subtask 4 (20 pts): $B \gt C$
Subtask 5 (20 pts): $N \leq 1000$.
Subtask 6 (30 pts): No additional constraints.

Sample Test Cases

Input Output
10 3
1 5 7 9
No

In the first sample, the baguette has length $N=10$.
Wasabi is at $[1, 5]$ (length 4). Peanut Butter is at $[7, 9]$ (length 2).
The gaps are length 1, 2, and 1. None are $\ge 3$.

0        1                                5                7                9        10
|--------|////////////////////////////////|----------------|////////////////|--------|
    OK                 Wasabi                    OK          Peanut Butter      OK
 (1 unit)            (4 units)                (2 units)        (2 units)     (1 unit)
10 3
1 5 4 7
Yes
Click to copy.

Scoring: Per Subtask
Authored by wy24180
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