Score : $400$ points

Problem Statement

There is a sequence $A=(A_0,\ldots,A_{N-1})$ of length $N$. Determine if there exists a tuple of integers $(x,y,z,w)$ that satisfies all of the following conditions:

• $0 \leq x < y < z < w \leq N$
• $A_x + A_{x+1} + \ldots + A_{y-1} = P$
• $A_y + A_{y+1} + \ldots + A_{z-1} = Q$
• $A_z + A_{z+1} + \ldots + A_{w-1} = R$

Constraints

• $3 \leq N \leq 2\times 10^5$
• $1 \leq A_i \leq 10^9$
• $1 \leq P,Q,R \leq 10^{15}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $P$ $Q$ $R$

$A_0$ $A_1$ $\ldots$ $A_{N-1}$

Output

If there exists a tuple that satisfies the conditions, print Yes; otherwise, print No.

10 5 7 5
1 3 2 2 2 3 1 4 3 2

Yes

$(x,y,z,w)=(1,3,6,8)$ satisfies the conditions.

9 100 101 100
31 41 59 26 53 58 97 93 23

No

7 1 1 1
1 1 1 1 1 1 1

Yes