human
PYTHON3 solution for "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.":


 ... What is a Python program to print "NO" if there are no such strings?
assistant
#Here is Python program to print "NO" if there are no such strings.
 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")