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: import jdk.dynalink.beans.StaticClass;
  
  import java.util.*;
  import java.io.*;
  
  public class CombinatoricsHomework {
      PrintWriter out;
      StringTokenizer st;
      BufferedReader br;
      final int imax = Integer.MAX_VALUE, imin = Integer.MIN_VALUE;
      final int mod = 1000000007;
  
      void solve() throws Exception {
          int t = 1;
          t = ni();
          for (int ii = 0; ii < t; ii++) {
              int[] a= ni(3); int m= ni();
              Arrays.sort(a);
  
              print(m>= a[2]-a[1]-a[0]-1 && m<= a[0]+a[1]+a[2]-3);
          }
      }
  
      public static void main(String[] args) throws Exception {
          new CombinatoricsHomework().run();
      }
  
      void run() throws Exception {
          if (System.getProperty("ONLINE_JUDGE") == null) {
              File file = new File("./input.txt");
              br = new BufferedReader(new FileReader(file));
              out = new PrintWriter("./output.txt");
          } else {
              out = new PrintWriter(System.out);
              br = new BufferedReader(new InputStreamReader(System.in));
          }
  
          long ss = System.currentTimeMillis();
          st = new StringTokenizer("");
          while (true) {
              try {
                  solve();
              } catch (Exception e) {
                  e.printStackTrace(out);
              } catch (StackOverflowError e) {
                  e.printStackTrace(out);
              }
  
              String s = br.readLine();
              if (s == null) break;
              else st = new StringTokenizer(s);
          }
          //out.println(System.currentTimeMillis()-ss+"ms");
          out.flush();
      }
  
      void read() throws Exception {
          st = new StringTokenizer(br.readLine());
      }
  
      int ni() throws Exception {
          if (!st.hasMoreTokens()) read();
          return Integer.parseInt(st.nextToken());
      }
  
      char nc() throws Exception {
          if (!st.hasMoreTokens()) read();
          return st.nextToken().charAt(0);
      }
  
      String nw() throws Exception {
          if (!st.hasMoreTokens()) read();
          return st.nextToken();
      }
  
      long nl() throws Exception {
          if (!st.hasMoreTokens()) read();
          return Long.parseLong(st.nextToken());
      }
  
      int[] ni(int n) throws Exception {
          int[] ret = new int[n];
          for (int i = 0; i < n; i++) ret[i] = ni();
          return ret;
      }
  
      long[] nl(int n) throws Exception {
          long[] ret = new long[n];
          for (int i = 0; i < n; i++) ret[i] = nl();
          return ret;
      }
  
      double nd() throws Exception {
          if (!st.hasMoreTokens()) read();
          return Double.parseDouble(st.nextToken());
      }
  
      String ns() throws Exception {
          String s = br.readLine();
          return s.length() == 0 ? br.readLine() : s;
      }
  
      void print(int[] arr) {
          for (int i : arr) out.print(i + " ");
          out.println();
      }
  
      void print(long[] arr) {
          for (long i : arr) out.print(i + " ");
          out.println();
      }
  
      void print(int[][] arr) {
          for (int[] i : arr) {
              for (int j : i) out.print(j + " ");
              out.println();
          }
      }
  
      void print(long[][] arr) {
          for (long[] i : arr) {
              for (long j : i) out.print(j + " ");
              out.println();
          }
      }
  
      long add(long a, long b) {
          if (a + b >= mod) return (a + b) - mod;
          else return a + b >= 0 ? a + b : a + b + mod;
      }
  
      long mul(long a, long b) {
          return (a * b) % mod;
      }
  
      void print(boolean b) {
          if (b) out.println("YES");
          else out.println("NO");
      }
  
      long binExp(long base, long power) {
          long res = 1l;
          while (power != 0) {
              if ((power & 1) == 1) res = mul(res, base);
              base = mul(base, base);
              power >>= 1;
          }
          return res;
      }
  
      long gcd(long a, long b) {
          if (b == 0) return a;
          else return gcd(b, a % b);
      }
  
      // strictly smaller on left
      void stack_l(int[] arr, int[] left) {
          Stack<Integer> stack = new Stack<>();
          for (int i = 0; i < arr.length; i++) {
              while (!stack.isEmpty() && arr[stack.peek()] >= arr[i]) stack.pop();
              if (stack.isEmpty()) left[i] = -1;
              else left[i] = stack.peek();
              stack.push(i);
          }
      }
  
      // strictly smaller on right
      void stack_r(int[] arr, int[] right) {
          Stack<Integer> stack = new Stack<>();
          for (int i = arr.length - 1; i >= 0; i--) {
              while (!stack.isEmpty() && arr[stack.peek()] >= arr[i]) stack.pop();
              if (stack.isEmpty()) right[i] = arr.length;
              else right[i] = stack.peek();
              stack.push(i);
          }
      }
  
      private void sort(int[] arr) {
          List<Integer> list = new ArrayList<>();
          for (int i : arr) list.add(i);
          Collections.sort(list);
          for (int i = 0; i < arr.length; i++) arr[i] = list.get(i);
      }
  }