human
You are given four integer values a, b, c and m.

Check if there exists a string that contains: 

  * a letters 'A'.

  * b letters 'B'.

  * c letters 'C'.

  * no other letters.

  * exactly m pairs of adjacent equal letters (exactly m such positions i that the i-th letter is equal to the (i+1)-th one). 

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of testcases.

Each of the next t lines contains the description of the testcase — four integers a, b, c and m (1 ≤ a, b, c ≤ 10^8.
0 ≤ m ≤ 10^8).

Output

For each testcase print "YES" if there exists a string that satisfies all the requirements. Print "NO" if there are no such strings.

You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).

Example

Input

3
2 2 1 0
1 1 1 1
1 2 3 2

Output

YES
NO
YES

Note

In the first testcase strings "ABCAB" or "BCABA" satisfy the requirements. There exist other possible strings.

In the second testcase there's no way to put adjacent equal letters if there's no letter that appears at least twice.

In the third testcase string "CABBCC" satisfies the requirements. There exist other possible strings.
Using python can you solve the prior task?

=====
Can you provide a Python code to print "NO" if there are no such strings?
assistant
#Here is Python code to print "NO" if there are no such strings.

import sys
testing = len(sys.argv) == 4 and sys.argv[3] == "myTest"
interactive = False
if testing:
    cmd = sys.stdout
    from time import time
    start_time = int(round(time() * 1000)) 
    readAll = open(sys.argv[1], 'r').read
    sys.stdout = open(sys.argv[2], 'w')
else:
    readAll = sys.stdin.read

# ############ ---- I/O Functions ---- ############

class InputData:
    def __init__(self):
        self.lines = readAll().split('\n')
        self.n = len(self.lines)
        self.ii = -1
    def input(self):
        self.ii += 1
        assert self.ii < self.n
        return self.lines[self.ii]

flush = sys.stdout.flush
if interactive and not testing:
    input = sys.stdin.readline
else:
    inputData = InputData()
    input = inputData.input

def intin():
    return(int(input()))
def intlin():
    return(list(map(int,input().split())))
def chrin():
    return(list(input()))
def strin():
    return input()
def lout(l, sep="\n", toStr=True):
    print(sep.join(map(str, l) if toStr else l))
def dout(*args, **kargs):
    if not testing: return
    if args: print(args[0] if len(args)==1 else args)
    if kargs: print([(k,v) for k,v in kargs.items()])
def ask(q):
    sys.stdout.write(str(q)+'\n')
    flush()
    return intin()
    
# ############ ---- I/O Functions ---- ############

# from math import ceil
# from collections import defaultdict as ddict, Counter
# from heapq import *
# from Queue import Queue

def main():
    a,b,c,m = intlin()
    if max(a-1,0)+max(b-1,0)+max(c-1,0) < m:
        return False
    a,b,c = sorted([a,b,c])

    k = min(m, c-b)
    m -= k
    c -= k

    k = min(m/2, b-a)
    b -= k
    c -= k
    m -= k*2

    if m == 0:
        return a+b+1 >= c
    return max(a-1,0)+max(b-1,0)+max(c-1,0) >= m





anss = []
for _ in xrange(intin()):
    anss.append("YES" if main() else "NO")
lout(anss)

if testing:
    sys.stdout = cmd
    print(int(round(time() * 1000))  - start_time)