#include <bits/stdc++.h>
#pragma GCC optimize("O3")
namespace fastinput {
template <class T = int>
inline T readInt();
inline long double readDouble();
inline int readUInt();
inline int readChar();
inline void readWord(char *s);
inline bool readLine(char *s);
inline bool isEof();
inline int peekChar();
inline bool seekEof();
template <class T>
inline void writeInt(T x, int len = -1);
template <class T>
inline void writeUInt(T x, int len = -1);
inline void writeChar(int x);
inline void writeWord(const char *s);
inline void writeDouble(long double x, int len = 0);
inline void flush();
static const int buf_size = 4096;
static char buf[buf_size];
static int buf_len = 0, buf_pos = 0;
inline bool isEof() {
  if (buf_pos == buf_len) {
    buf_pos = 0, buf_len = fread(buf, 1, buf_size, stdin);
    if (buf_pos == buf_len) return 1;
  }
  return 0;
}
inline int getChar() { return isEof() ? -1 : buf[buf_pos++]; }
inline int peekChar() { return isEof() ? -1 : buf[buf_pos]; }
inline bool seekEof() {
  int c;
  while ((c = peekChar()) != -1 && c <= 32) buf_pos++;
  return c == -1;
}
inline int readChar() {
  int c = getChar();
  while (c != -1 && c <= 32) c = getChar();
  return c;
}
inline int readUInt() {
  int c = readChar(), x = 0;
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return x;
}
template <class T>
inline T readInt() {
  int s = 1, c = readChar();
  T x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return s == 1 ? x : -x;
}
inline long double readDouble() {
  int s = 1, c = readChar();
  long double x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  if (c == '.') {
    c = getChar();
    long double coef = 1;
    while ('0' <= c && c <= '9') x += (c - '0') * (coef *= 0.1), c = getChar();
  }
  return s == 1 ? x : -x;
}
inline void readWord(char *s) {
  int c = readChar();
  while (c > 32) *s++ = (char)c, c = getChar();
  *s = 0;
}
inline bool readLine(char *s) {
  int c = getChar();
  while (c != '\n' && c != -1) *s++ = (char)c, c = getChar();
  *s = 0;
  return c != -1;
}
static int write_buf_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x) {
  if (write_buf_pos == buf_size)
    fwrite(write_buf, 1, buf_size, stdout), write_buf_pos = 0;
  write_buf[write_buf_pos++] = (char)x;
}
inline void flush() {
  if (write_buf_pos)
    fwrite(write_buf, 1, write_buf_pos, stdout), write_buf_pos = 0;
}
template <class T>
inline void writeInt(T x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = '0' + x % 10, x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
}
template <class T>
inline void writeUInt(T x, int output_len) {
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = (char)('0' + (char)(x % 10)), x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
}
inline void writeWord(const char *s) {
  while (*s) writeChar(*s++);
}
inline void writeDouble(long double x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  int t = (int)x;
  writeUInt(t), x -= t;
  writeChar('.');
  for (int i = output_len - 1; i > 0; i--) {
    x *= 10;
    t = std::min(9, (int)x);
    writeChar('0' + t), x -= t;
  }
  x *= 10;
  t = std::min(9, (int)(x + 0.5));
  writeChar('0' + t);
}
}  // namespace fastinput
using namespace fastinput;
using namespace std;
const int MAX_MEM = 2e8;
int mpos = 0;
char mem[MAX_MEM];
inline void *operator new(size_t n) {
  mpos += n;
  return (void *)(mem + mpos - n);
}
inline void operator delete(void *) noexcept {}
const int N = 1e5;
vector<int> arr[N];
set<pair<int, int> > bad;
const int NM = 1e5 + 1;
int perm[NM];
int shift[NM];
int modulo[NM];
int n, m;
int check(int a, int b) {
  int rowa = a / m;
  int rowb = b / m;
  if (a > b) swap(a, b);
  if (a + m == b) return 1;
  if (b == a + 1 && modulo[a + 1] != 0) return 1;
  return 0;
}
const int CAP = 3;
int main() {
  srand(228);
  ::ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int val = 0; val <= n * m; ++val) modulo[val] = val % m;
  for (int i = 0; i < n; ++i) {
    arr[i].resize(m);
  }
  for (int i = 0; i < n * m; ++i) {
    perm[i] = i;
  }
  const int len = n * m;
  random_shuffle(perm, perm + len);
  int iter = 2e5;
  int x = 0, y = 0;
  int cnt = 0;
  while (iter--) {
    swap(perm[cnt], perm[cnt + rand() % (len - cnt)]);
    arr[x][y] = perm[cnt];
    bool rollback = false;
    if (y > 0) {
      rollback |= check(arr[x][y], arr[x][y - 1]);
    }
    if (x > 0) {
      rollback |= check(arr[x - 1][y], arr[x][y]);
    }
    if (!rollback) {
      cnt++;
      ++y;
      if (y == m) y = 0, ++x;
      if (x == n) {
        cout << "YES\n";
        for (int i = 0; i < n; ++i) {
          for (int j = 0; j < m; ++j) {
            cout << arr[i][j] + 1 << " ";
          }
          cout << endl;
        }
        return 0;
      }
    } else {
      if (shift[cnt]++ > CAP) {
        shift[cnt] = 0;
        if (cnt == 0) {
          random_shuffle(perm, perm + len);
        }
        --cnt;
        if (y == 0)
          --x, y = m - 1;
        else
          --y;
      }
    }
  }
  cout << "NO\n";
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Students went into a class to write a test and sat in some way. The teacher thought: "Probably they sat in this order to copy works of each other. I need to rearrange them in such a way that students that were neighbors are not neighbors in a new seating."

The class can be represented as a matrix with n rows and m columns with a student in each cell. Two students are neighbors if cells in which they sit have a common side.

Let's enumerate students from 1 to n·m in order of rows. So a student who initially sits in the cell in row i and column j has a number (i - 1)·m + j. You have to find a matrix with n rows and m columns in which all numbers from 1 to n·m appear exactly once and adjacent numbers in the original matrix are not adjacent in it, or determine that there is no such matrix.

Input

The only line contains two integers n and m (1 ≤ n, m ≤ 105; n·m ≤ 105) — the number of rows and the number of columns in the required matrix.

Output

If there is no such matrix, output "NO" (without quotes). 

Otherwise in the first line output "YES" (without quotes), and in the next n lines output m integers which form the required matrix.

Examples

Input

2 4


Output

YES
5 4 7 2 
3 6 1 8 


Input

2 1


Output

NO

Note

In the first test case the matrix initially looks like this:
    
    
      
    1 2 3 4  
    5 6 7 8  
    

It's easy to see that there are no two students that are adjacent in both matrices.

In the second test case there are only two possible seatings and in both of them students with numbers 1 and 2 are neighbors.

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
namespace fastinput {
template <class T = int>
inline T readInt();
inline long double readDouble();
inline int readUInt();
inline int readChar();
inline void readWord(char *s);
inline bool readLine(char *s);
inline bool isEof();
inline int peekChar();
inline bool seekEof();
template <class T>
inline void writeInt(T x, int len = -1);
template <class T>
inline void writeUInt(T x, int len = -1);
inline void writeChar(int x);
inline void writeWord(const char *s);
inline void writeDouble(long double x, int len = 0);
inline void flush();
static const int buf_size = 4096;
static char buf[buf_size];
static int buf_len = 0, buf_pos = 0;
inline bool isEof() {
  if (buf_pos == buf_len) {
    buf_pos = 0, buf_len = fread(buf, 1, buf_size, stdin);
    if (buf_pos == buf_len) return 1;
  }
  return 0;
}
inline int getChar() { return isEof() ? -1 : buf[buf_pos++]; }
inline int peekChar() { return isEof() ? -1 : buf[buf_pos]; }
inline bool seekEof() {
  int c;
  while ((c = peekChar()) != -1 && c <= 32) buf_pos++;
  return c == -1;
}
inline int readChar() {
  int c = getChar();
  while (c != -1 && c <= 32) c = getChar();
  return c;
}
inline int readUInt() {
  int c = readChar(), x = 0;
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return x;
}
template <class T>
inline T readInt() {
  int s = 1, c = readChar();
  T x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  return s == 1 ? x : -x;
}
inline long double readDouble() {
  int s = 1, c = readChar();
  long double x = 0;
  if (c == '-') s = -1, c = getChar();
  while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getChar();
  if (c == '.') {
    c = getChar();
    long double coef = 1;
    while ('0' <= c && c <= '9') x += (c - '0') * (coef *= 0.1), c = getChar();
  }
  return s == 1 ? x : -x;
}
inline void readWord(char *s) {
  int c = readChar();
  while (c > 32) *s++ = (char)c, c = getChar();
  *s = 0;
}
inline bool readLine(char *s) {
  int c = getChar();
  while (c != '\n' && c != -1) *s++ = (char)c, c = getChar();
  *s = 0;
  return c != -1;
}
static int write_buf_pos = 0;
static char write_buf[buf_size];
inline void writeChar(int x) {
  if (write_buf_pos == buf_size)
    fwrite(write_buf, 1, buf_size, stdout), write_buf_pos = 0;
  write_buf[write_buf_pos++] = (char)x;
}
inline void flush() {
  if (write_buf_pos)
    fwrite(write_buf, 1, write_buf_pos, stdout), write_buf_pos = 0;
}
template <class T>
inline void writeInt(T x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = '0' + x % 10, x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
}
template <class T>
inline void writeUInt(T x, int output_len) {
  char s[24];
  int n = 0;
  while (x || !n) s[n++] = (char)('0' + (char)(x % 10)), x /= 10;
  while (n < output_len) s[n++] = '0';
  while (n--) writeChar(s[n]);
}
inline void writeWord(const char *s) {
  while (*s) writeChar(*s++);
}
inline void writeDouble(long double x, int output_len) {
  if (x < 0) writeChar('-'), x = -x;
  int t = (int)x;
  writeUInt(t), x -= t;
  writeChar('.');
  for (int i = output_len - 1; i > 0; i--) {
    x *= 10;
    t = std::min(9, (int)x);
    writeChar('0' + t), x -= t;
  }
  x *= 10;
  t = std::min(9, (int)(x + 0.5));
  writeChar('0' + t);
}
}  // namespace fastinput
using namespace fastinput;
using namespace std;
const int MAX_MEM = 2e8;
int mpos = 0;
char mem[MAX_MEM];
inline void *operator new(size_t n) {
  mpos += n;
  return (void *)(mem + mpos - n);
}
inline void operator delete(void *) noexcept {}
const int N = 1e5;
vector<int> arr[N];
set<pair<int, int> > bad;
const int NM = 1e5 + 1;
int perm[NM];
int shift[NM];
int modulo[NM];
int n, m;
int check(int a, int b) {
  int rowa = a / m;
  int rowb = b / m;
  if (a > b) swap(a, b);
  if (a + m == b) return 1;
  if (b == a + 1 && modulo[a + 1] != 0) return 1;
  return 0;
}
const int CAP = 3;
int main() {
  srand(228);
  ::ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int val = 0; val <= n * m; ++val) modulo[val] = val % m;
  for (int i = 0; i < n; ++i) {
    arr[i].resize(m);
  }
  for (int i = 0; i < n * m; ++i) {
    perm[i] = i;
  }
  const int len = n * m;
  random_shuffle(perm, perm + len);
  int iter = 2e5;
  int x = 0, y = 0;
  int cnt = 0;
  while (iter--) {
    swap(perm[cnt], perm[cnt + rand() % (len - cnt)]);
    arr[x][y] = perm[cnt];
    bool rollback = false;
    if (y > 0) {
      rollback |= check(arr[x][y], arr[x][y - 1]);
    }
    if (x > 0) {
      rollback |= check(arr[x - 1][y], arr[x][y]);
    }
    if (!rollback) {
      cnt++;
      ++y;
      if (y == m) y = 0, ++x;
      if (x == n) {
        cout << "YES\n";
        for (int i = 0; i < n; ++i) {
          for (int j = 0; j < m; ++j) {
            cout << arr[i][j] + 1 << " ";
          }
          cout << endl;
        }
        return 0;
      }
    } else {
      if (shift[cnt]++ > CAP) {
        shift[cnt] = 0;
        if (cnt == 0) {
          random_shuffle(perm, perm + len);
        }
        --cnt;
        if (y == 0)
          --x, y = m - 1;
        else
          --y;
      }
    }
  }
  cout << "NO\n";
  return 0;
}

```