description: 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.
solution: try:
          import sys
          from functools import lru_cache, cmp_to_key
          from heapq import merge, heapify, heappop, heappush
          from math import *
          from collections import defaultdict as dd, deque, Counter as C
          from itertools import combinations as comb, permutations as perm
          from bisect import bisect_left as bl, bisect_right as br, bisect, insort
          from time import perf_counter
          from fractions import Fraction
          import copy
          from copy import deepcopy
          import time
          starttime = time.time()
          mod = int(pow(10, 9) + 7)
          mod2 = 998244353
  
          def data(): return sys.stdin.readline().strip()
          def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
          def L(): return list(sp())
          def sl(): return list(ssp())
          def sp(): return map(int, data().split())
          def ssp(): return map(str, data().split())
          def l1d(n, val=0): return [val for i in range(n)]
          def l2d(n, m, val=0): return [l1d(n, val) for j in range(m)]
          def A2(n,m): return [[0]*m for i in range(n)]
          def A(n):return [0]*n
          # input = stdin.buffer.readline
          # I = lambda : list(map(int,input().split()))
          # import sys
          # input=sys.stdin.readline
          
  
          sys.stdin = open("input.txt", "r")
          sys.stdout = open("output.txt", "w")
  except:
          pass
  
  
  
  for _ in range(L()[0]):
          a,b,c,m = L()
          a,b,c=sorted([a,b,c])
          mn = max(0,c-(a+b+1))
          mx = a+b+c-3
          if not mn<=m<=mx:
                  print("NO")
          else:
                  print("YES")