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 java.util.*;
  import java.lang.*;
  import java.math.BigInteger;
  
  import java.io.*;
  
  public class Main implements Runnable {
  
      public static void main(String[] args) {
          new Thread(null, new Main(), "whatever", 1 << 26).start();
      }
  
  
      private FastScanner sc;
      private PrintWriter pw;
  
      public void run() {
          try {
              // pw = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
              // sc = new FastScanner(new BufferedReader(new FileReader("input.txt")));
              pw = new PrintWriter(System.out);
              sc = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
          } catch (Exception e) {
              throw new RuntimeException();
          }
          int t = sc.nextInt();
          // int t = 1;
          while (t-- > 0) {
              // sc.nextLine();
              solve();
          }
          pw.close();
      }
  
      public long mod = 1_000_000_007;
  
      public class Num {
          char ch;
          int n;
  
          Num(char ch, int n) {
              this.ch = ch;
              this.n = n;
          }
      }
  
      public void solve() {
          Num[] arr = new Num[3];
  
          arr[0] = new Num('A', sc.nextInt());
          arr[1] = new Num('B', sc.nextInt());
          arr[2] = new Num('C', sc.nextInt());
  
          int m = sc.nextInt();
  
          Arrays.sort(arr, (o1, o2)-> {
              return o1.n - o2.n;
          });
  
          // helper(arr, m, 'q');
  
          Arrays.sort(arr, (o1, o2)-> {
              return o1.n - o2.n;
          });
  
          if (m > arr[0].n + arr[1].n + arr[2].n - 3) {
              pw.println("NO");
              return;
          }
          int min = 0;
          if (arr[2].n - arr[1].n - arr[0].n >= 2) {
              min = arr[2].n - arr[1].n - arr[0].n - 1;
          }
  
          int max = arr[0].n + arr[1].n + arr[2].n - 3;
  
          if (m >= min && m <= max) {
              pw.println("YES");
          } else pw.println("NO");
      }
  
      // public void helper(Num[] arr, int m, char last) {
      //     if (m == 0) return;
      //     Arrays.sort(arr, (o1, o2)-> {
      //         return o1.n - o2.n;
      //     });
      //     if (last == arr[2].ch) {
      //         // pw.println("After reducing 1 from arr[2].ch = " + arr[2].ch + " and arr[2].n = " + arr[2].n);
      //         arr[2].n--;
      //         if (arr[2].n < 0) return;
      //         // Arrays.sort(arr, (o1, o2)-> {
      //         //     return o1.n - o2.n;
      //         // });
      //         helper(arr, m - 1, last);
      //         return;
      //     }
      //     // pw.println("After reducing 2 from arr[2].ch = " + arr[2].ch + " and arr[2].n = " + arr[2].n);
      //     arr[2].n -= 2;
      //     if (arr[2].n < 0) return;
      //     helper(arr, m - 1, arr[2].ch);
      // }
  
      // public void helper2(Num[] arr, char last) {
      //     Arrays.sort(arr, (o1, o2)-> {
      //         return o1.n - o2.n;
      //     });
      //     if (arr[0].n == 0) {
      //         if (arr[2].n - arr[1].n == 0) {
      //             pw.println("YES");
      //         } else if (arr[2].n - arr[1].n == 1 && last != arr[2].ch) {
      //             pw.println("YES");
      //         } else pw.println("NO");
      //         return;
      //     }
  
      //     if (last != arr[2].ch) {
      //         arr[2].n--;
      //         helper2(arr, arr[2].ch);
      //         return;
      //     }
  
      //     arr[1].n--;
      //     helper2(arr, arr[1].ch);
      // }
  
  
      class FastScanner {
          private BufferedReader reader = null;
          private StringTokenizer tokenizer = null;
  
          public FastScanner(BufferedReader bf) {
              reader = bf;
              tokenizer = null;
          }
  
          public String next() {
              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      tokenizer = new StringTokenizer(reader.readLine());
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken();
          }
  
          public String nextLine() {
              if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      return reader.readLine();
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken("\n");
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
          public float nextFloat() {
              return Float.parseFloat(next());
          }
  
          public int[] nextIntArray(int n) {
              int[] a = new int[n];
              for (int i = 0; i < n; i++) {
                  a[i] = nextInt();
              }
              return a;
          }
  
          public String[] nextStringArray(int n) {
              String[] a = new String[n];
              for (int i = 0; i < n; i++) {
                  a[i] = next();
              }
              return a;
          }
  
          public long[] nextLongArray(int n) {
              long[] a = new long[n];
              for (int i = 0; i < n; i++) {
                  a[i] = nextLong();
              }
              return a;
          }
  
      }
  
      public long fastPow(long x, long y, long mod) {
          if (y == 0) return 1;
          if (y == 1) return x % mod;
  
          long temp = fastPow(x, y / 2, mod);
          long ans = (temp * temp) % mod;
  
          return (y % 2 == 1) ? (ans * (x % mod)) % mod : ans;
      }
  
      // public long fastPow(long x, long y) {
      //     if (y == 0) return 1;
      //     if (y == 1) return x;
  
      //     long temp = fastPow(x, y / 2);
      //     long ans = (temp * temp);
  
      //     return (y % 2 == 1) ? (ans * x) : ans;
      // }
  
  }
  