D. XP Challenge
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The Iguanodon, "Iggy" the Iguagua, is escaping Jurassic Park. She begins with $$$N$$$ initial XP. Attacking opponents with her "thumb spike" attack deals $$$P_1$$$ damage to her opponent and costs $$$P_2$$$ damage to her own XP, and she can use this move at most once for each opponent. She can use the "charge" attack an unlimited number of times, dealing $$$Q_1$$$ damage to her opponent with a cost of $$$Q_2$$$ to her own XP. Along her escape route is a series of $$$M$$$ small dinosaurs, each having an initial XP of $$$a_i \: (1 \leq i \leq M)$$$. A dinosaur is considered defeated when they have no positive XP left. Determine if Iggy can defeat all the dinosaurs blocking her route using her attacks without being defeated herself.

Input

The first line contains integers $$$N (1\leq N \leq 10^9)$$$, the initial XP, and $$$M (1\leq M \leq 10^5)$$$, the total number of opponents.

The second line has integers $$$P_1 (1\leq P_1 \leq 10^9)$$$ and $$$P_2 (1\leq P_2 \leq 10^9)$$$, the cost of the "thumb spike" attack.

The third line has integers $$$Q_1 (1\leq Q_1 \leq 10^9)$$$ and $$$Q_2 (1\leq Q_2 \leq 10^9)$$$, the cost of the "charge" attack.

The last line contains $$$M$$$ integers $$$a_1, a_2, \cdots a_M (1\leq a_i \leq 10^9)$$$ denoting the XP of each opponent.

Output

Print "YES" if Iggy can escape the park with positive remaining XP, otherwise print "NO".

Example
Input
8 3
5 2
3 1
5 8 6
Output
YES