description: The only difference between this problem and D1 is that you don't have to provide the way to construct the answer in D1, but you have to do it in this problem.
  
  There's a table of n × m cells (n rows and m columns). The value of n ⋅ m is even.
  
  A domino is a figure that consists of two cells having a common side. It may be horizontal (one of the cells is to the right of the other) or vertical (one of the cells is above the other).
  
  You need to place nm/2 dominoes on the table so that exactly k of them are horizontal and all the other dominoes are vertical. The dominoes cannot overlap and must fill the whole table.
  
  Input
  
  The first line contains one integer t (1 ≤ t ≤ 10) — the number of test cases. Then t test cases follow.
  
  Each test case consists of a single line. The line contains three integers n, m, k (1 ≤ n,m ≤ 100, 0 ≤ k ≤ nm/2, n ⋅ m is even) — the count of rows, columns and horizontal dominoes, respectively.
  
  Output
  
  For each test case:
  
    * print "NO" if it's not possible to place the dominoes on the table in the described way; 
    * otherwise, print "YES" on a separate line, then print n lines so that each of them contains m lowercase letters of the Latin alphabet — the layout of the dominoes on the table. Each cell of the table must be marked by the letter so that for every two cells having a common side, they are marked by the same letters if and only if they are occupied by the same domino. I.e. both cells of the same domino must be marked with the same letter, but two dominoes that share a side must be marked with different letters. If there are multiple solutions, print any of them. 
  
  Example
  
  Input
  
  
  8
  4 4 2
  2 3 0
  3 2 3
  1 2 0
  2 4 2
  5 2 2
  2 17 16
  2 1 1
  
  
  Output
  
  
  YES
  accx
  aegx
  bega
  bdda
  YES
  aha
  aha
  YES
  zz
  aa
  zz
  NO
  YES
  aaza
  bbza
  NO
  YES
  bbaabbaabbaabbaay
  ddccddccddccddccy
  NO
solution: import java.io.*;
  import java.util.*;
  
  import static java.lang.Math.*;
  import static java.util.Arrays.*;
  
  public class cf1551d2_2 {
  
      public static void main(String[] args) throws IOException {
          int t = ri();
          while (t --> 0) {
              int n = rni(), m = ni(), k = ni();
              if (n % 2 == 0 && m % 2 == 0) {
                  if (prYN(k % 2 == 0)) {
                      char[][] ans = new char[n][m];
                      int i = 0, j = 0;
                      while (k --> 0) {
                          char c = get_hor(ans, i, j, n, m);
                          ans[i][j] = ans[i][j + 1] = c;
                          if (++i == n) {
                              j += 2;
                              i = 0;
                          }
                      }
                      while (j < m) {
                          char c = get_ver(ans, i, j, n, m);
                          ans[i][j] = ans[i + 1][j] = c;
                          c = get_ver(ans, i, j + 1, n, m);
                          ans[i][j + 1] = ans[i + 1][j + 1] = c;
                          if ((i += 2) == n) {
                              j += 2;
                              i = 0;
                          }
                      }
                      for (char[] row : ans) {
                          prln(row);
                      }
                  }
              } else if (n % 2 == 1 && m % 2 == 0) {
                  if (prYN(k >= m / 2 && (k - m / 2) % 2 == 0)) {
                      char[][] ans = new char[n][m];
                      for (int i = 0; i < m; i += 2) {
                          char c = get_hor(ans, 0, i, n, m);
                          ans[0][i] = ans[0][i + 1] = c;
                          --k;
                      }
                      if (n > 1) {
                          int i = 1, j = 0;
                          while (k --> 0) {
                              char c = get_hor(ans, i, j, n, m);
                              ans[i][j] = ans[i][j + 1] = c;
                              if (++i == n) {
                                  j += 2;
                                  i = 1;
                              }
                          }
                          while (j < m) {
                              char c = get_ver(ans, i, j, n, m);
                              ans[i][j] = ans[i + 1][j] = c;
                              c = get_ver(ans, i, j + 1, n, m);
                              ans[i][j + 1] = ans[i + 1][j + 1] = c;
                              if ((i += 2) == n) {
                                  j += 2;
                                  i = 1;
                              }
                          }
                      }
                      for (char[] row : ans) {
                          prln(row);
                      }
                  }
              } else {
                  if (prYN(k <= n * (m - 1) / 2 && (n * (m - 1) / 2 - k) % 2 == 0)) {
                      char[][] ans = new char[n][m];
                      for (int i = 0; i < n; i += 2) {
                          char c = get_ver(ans, i, 0, n, m);
                          ans[i][0] = ans[i + 1][0] = c;
                      }
                      int i = 0, j = 1;
                      if (m > 1) {
                          while (k --> 0) {
                              char c = get_hor(ans, i, j, n, m);
                              ans[i][j] = ans[i][j + 1] = c;
                              if (++i == n) {
                                  j += 2;
                                  i = 0;
                              }
                          }
                          while (j < m) {
                              char c = get_ver(ans, i, j, n, m);
                              ans[i][j] = ans[i + 1][j] = c;
                              c = get_ver(ans, i, j + 1, n, m);
                              ans[i][j + 1] = ans[i + 1][j + 1] = c;
                              if ((i += 2) == n) {
                                  j += 2;
                                  i = 0;
                              }
                          }
                      }
                      for (char[] row : ans) {
                          prln(row);
                      }
                  }
              }
          }
          close();
      }
  
      static char get_ver(char[][] map, int i, int j, int n, int m) {
          List<Character> list = new ArrayList<>();
          if (i > 0) {
              list.add(map[i - 1][j]);
          }
          if (j < m - 1) {
              list.add(map[i][j + 1]);
              list.add(map[i + 1][j + 1]);
          }
          if (i < n - 2) {
              list.add(map[i + 2][j]);
          }
          if (j > 0) {
              list.add(map[i][j - 1]);
              list.add(map[i + 1][j - 1]);
          }
          list.sort(Character::compare);
          char ans = 'a';
          for (char c : list) {
              if (ans == c) {
                  ++ans;
              }
          }
          return ans;
      }
  
      static char get_hor(char[][] map, int i, int j, int n, int m) {
          List<Character> list = new ArrayList<>();
          if (i > 0) {
              list.add(map[i - 1][j]);
              list.add(map[i - 1][j + 1]);
          }
          if (j < m - 2) {
              list.add(map[i][j + 2]);
          }
          if (i < n - 1) {
              list.add(map[i + 1][j]);
              list.add(map[i + 1][j + 1]);
          }
          if (j > 0) {
              list.add(map[i][j - 1]);
          }
          list.sort(Character::compare);
          char ans = 'a';
          for (char c : list) {
              if (ans == c) {
                  ++ans;
              }
          }
          return ans;
      }
  
      static BufferedReader __i = new BufferedReader(new InputStreamReader(System.in));
      static PrintWriter __o = new PrintWriter(new OutputStreamWriter(System.out));
      static StringTokenizer input;
      static Random __r = new Random();
  
      // references
      // IBIG = 1e9 + 7
      // IMAX ~= 2e9
      // LMAX ~= 9e18
  
      // constants
      static final int IBIG = 1000000007;
      static final int IMAX = 2147483647;
      static final long LMAX = 9223372036854775807L;
      // math util
      static int minof(int a, int b, int c) {return min(a, min(b, c));}
      static int minof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
      static long minof(long a, long b, long c) {return min(a, min(b, c));}
      static long minof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
      static int maxof(int a, int b, int c) {return max(a, max(b, c));}
      static int maxof(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
      static long maxof(long a, long b, long c) {return max(a, max(b, c));}
      static long maxof(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return max(x[0], x[1]); if (x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] > max) max = x[i]; return max;}
      static int powi(int a, int b) {if (a == 0) return 0; int ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
      static long powl(long a, int b) {if (a == 0) return 0; long ans = 1; while (b > 0) {if ((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
      static int fli(double d) {return (int) d;}
      static int cei(double d) {return (int) ceil(d);}
      static long fll(double d) {return (long) d;}
      static long cel(double d) {return (long) ceil(d);}
      static int gcd(int a, int b) {return b == 0 ? a : gcd(b, a % b);}
      static long gcd(long a, long b) {return b == 0 ? a : gcd(b, a % b);}
      static int[] exgcd(int a, int b) {if (b == 0) return new int[] {1, 0}; int[] y = exgcd(b, a % b); return new int[] {y[1], y[0] - y[1] * (a / b)};}
      static long[] exgcd(long a, long b) {if (b == 0) return new long[] {1, 0}; long[] y = exgcd(b, a % b); return new long[] {y[1], y[0] - y[1] * (a / b)};}
      static int randInt(int min, int max) {return __r.nextInt(max - min + 1) + min;}
      static long mix(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
      // array util
      static void reverse(int[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(long[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(double[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void reverse(char[] a) {for (int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
      static void shuffle(int[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void shuffle(long[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void shuffle(double[] a) {int n = a.length - 1; for (int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
      static void rsort(int[] a) {shuffle(a); sort(a);}
      static void rsort(long[] a) {shuffle(a); sort(a);}
      static void rsort(double[] a) {shuffle(a); sort(a);}
      static int[] copy(int[] a) {int[] ans = new int[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static long[] copy(long[] a) {long[] ans = new long[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static double[] copy(double[] a) {double[] ans = new double[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      static char[] copy(char[] a) {char[] ans = new char[a.length]; for (int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
      // input
      static void r() throws IOException {input = new StringTokenizer(rline());}
      static int ri() throws IOException {return Integer.parseInt(rline());}
      static long rl() throws IOException {return Long.parseLong(rline());}
      static double rd() throws IOException {return Double.parseDouble(rline());}
      static int[] ria(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni(); return a;}
      static void ria(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni();}
      static int[] riam1(int n) throws IOException {int[] a = new int[n]; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1; return a;}
      static void riam1(int[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = ni() - 1;}
      static long[] rla(int n) throws IOException {long[] a = new long[n]; r(); for (int i = 0; i < n; ++i) a[i] = nl(); return a;}
      static void rla(long[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nl();}
      static double[] rda(int n) throws IOException {double[] a = new double[n]; r(); for (int i = 0; i < n; ++i) a[i] = nd(); return a;}
      static void rda(double[] a) throws IOException {int n = a.length; r(); for (int i = 0; i < n; ++i) a[i] = nd();}
      static char[] rcha() throws IOException {return rline().toCharArray();}
      static void rcha(char[] a) throws IOException {int n = a.length, i = 0; for (char c : rline().toCharArray()) a[i++] = c;}
      static String rline() throws IOException {return __i.readLine();}
      static String n() {return input.nextToken();}
      static int rni() throws IOException {r(); return ni();}
      static int ni() {return Integer.parseInt(n());}
      static long rnl() throws IOException {r(); return nl();}
      static long nl() {return Long.parseLong(n());}
      static double rnd() throws IOException {r(); return nd();}
      static double nd() {return Double.parseDouble(n());}
      // output
      static void pr(int i) {__o.print(i);}
      static void prln(int i) {__o.println(i);}
      static void pr(long l) {__o.print(l);}
      static void prln(long l) {__o.println(l);}
      static void pr(double d) {__o.print(d);}
      static void prln(double d) {__o.println(d);}
      static void pr(char c) {__o.print(c);}
      static void prln(char c) {__o.println(c);}
      static void pr(char[] s) {__o.print(new String(s));}
      static void prln(char[] s) {__o.println(new String(s));}
      static void pr(String s) {__o.print(s);}
      static void prln(String s) {__o.println(s);}
      static void pr(Object o) {__o.print(o);}
      static void prln(Object o) {__o.println(o);}
      static void prln() {__o.println();}
      static void pryes() {prln("yes");}
      static void pry() {prln("Yes");}
      static void prY() {prln("YES");}
      static void prno() {prln("no");}
      static void prn() {prln("No");}
      static void prN() {prln("NO");}
      static boolean pryesno(boolean b) {prln(b ? "yes" : "no"); return b;};
      static boolean pryn(boolean b) {prln(b ? "Yes" : "No"); return b;}
      static boolean prYN(boolean b) {prln(b ? "YES" : "NO"); return b;}
      static void prln(int... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static void prln(long... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static void prln(double... a) {for (int i = 0, len = a.length - 1; i < len; pr(a[i]), pr(' '), ++i); if (a.length > 0) prln(a[a.length - 1]); else prln();}
      static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for (int i = 0; i < n; pr(iter.next()), pr(' '), ++i); if (n >= 0) prln(iter.next()); else prln();}
      static void h() {prln("hlfd"); flush();}
      static void flush() {__o.flush();}
      static void close() {__o.close();}
  }