#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
int fx[] = {+1, -1, +0, +0, +1, +1, -1, -1, +0};
int fy[] = {+0, +0, +1, -1, +1, -1, +1, -1, +0};
template <typename T>
inline T GCD(T a, T b) {
  a = abs(a);
  b = abs(b);
  while (b) {
    a = a % b;
    swap(a, b);
  }
  return a;
}
template <typename T>
inline T LCM(T x, T y) {
  T tp = GCD(x, y);
  if ((x / tp) * 1. * y > 9e18) return 9e18;
  return (x / tp) * y;
}
template <typename T>
inline T BigMod(T A, T B, T M) {
  T ret = 1;
  while (B) {
    if (B & 1) ret = (ret * A) % M;
    A = (A * A) % M;
    B = B >> 1;
  }
  return ret;
}
template <typename T>
inline T ModInv(T A, T M) {
  return BigMod(A, M - 2, M);
}
template <typename T>
bool scani(T &n) {
  n = 0;
  bool got = false;
  bool negative = false;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') negative = true;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    got = true;
    n = n * 10 + c - 48;
    c = getchar();
  }
  if (negative) n = ~(n - 1);
  return got;
}
template <typename T>
void write(T n, bool line = true) {
  if (n < 0) {
    putchar('-');
    n = -n;
  }
  if (!n) {
    putchar('0');
    if (line) putchar('\n');
    return;
  }
  char buff[22];
  int len = 0;
  while (n) buff[len++] = n % 10 + 48, n /= 10;
  for (int i = len - 1; i >= 0; i--) putchar(buff[i]);
  if (line) putchar('\n');
}
int scans(char *a) {
  int i = 0;
  char c = 0;
  while (c < 33) c = getchar();
  while (c > 33) {
    a[i++] = c;
    c = getchar();
  }
  a[i] = 0;
  return i;
}
int main() {
  int n, k;
  scani(n), scani(k);
  if (n < k || (n > 1 && k == 1)) {
    puts("-1");
    return 0;
  }
  int limit = max(0, k - 2);
  for (int i = 0; i + limit < n; i++) printf("%c", (i & 1) + 'a');
  for (int i = 2; i < k; i++) printf("%c", i + 'a');
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

Little penguin Polo adores strings. But most of all he adores strings of length n.

One day he wanted to find a string that meets the following conditions:

  1. The string consists of n lowercase English letters (that is, the string's length equals n), exactly k of these letters are distinct. 
  2. No two neighbouring letters of a string coincide; that is, if we represent a string as s = s1s2... sn, then the following inequality holds, si ≠ si + 1(1 ≤ i < n). 
  3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest. 



Help him find such string or state that such string doesn't exist.

String x = x1x2... xp is lexicographically less than string y = y1y2... yq, if either p < q and x1 = y1, x2 = y2, ... , xp = yp, or there is such number r (r < p, r < q), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1. The characters of the strings are compared by their ASCII codes.

Input

A single line contains two positive integers n and k (1 ≤ n ≤ 106, 1 ≤ k ≤ 26) — the string's length and the number of distinct letters.

Output

In a single line print the required string. If there isn't such string, print "-1" (without the quotes).

Examples

Input

7 4


Output

ababacd


Input

4 7


Output

-1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
int fx[] = {+1, -1, +0, +0, +1, +1, -1, -1, +0};
int fy[] = {+0, +0, +1, -1, +1, -1, +1, -1, +0};
template <typename T>
inline T GCD(T a, T b) {
  a = abs(a);
  b = abs(b);
  while (b) {
    a = a % b;
    swap(a, b);
  }
  return a;
}
template <typename T>
inline T LCM(T x, T y) {
  T tp = GCD(x, y);
  if ((x / tp) * 1. * y > 9e18) return 9e18;
  return (x / tp) * y;
}
template <typename T>
inline T BigMod(T A, T B, T M) {
  T ret = 1;
  while (B) {
    if (B & 1) ret = (ret * A) % M;
    A = (A * A) % M;
    B = B >> 1;
  }
  return ret;
}
template <typename T>
inline T ModInv(T A, T M) {
  return BigMod(A, M - 2, M);
}
template <typename T>
bool scani(T &n) {
  n = 0;
  bool got = false;
  bool negative = false;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') negative = true;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    got = true;
    n = n * 10 + c - 48;
    c = getchar();
  }
  if (negative) n = ~(n - 1);
  return got;
}
template <typename T>
void write(T n, bool line = true) {
  if (n < 0) {
    putchar('-');
    n = -n;
  }
  if (!n) {
    putchar('0');
    if (line) putchar('\n');
    return;
  }
  char buff[22];
  int len = 0;
  while (n) buff[len++] = n % 10 + 48, n /= 10;
  for (int i = len - 1; i >= 0; i--) putchar(buff[i]);
  if (line) putchar('\n');
}
int scans(char *a) {
  int i = 0;
  char c = 0;
  while (c < 33) c = getchar();
  while (c > 33) {
    a[i++] = c;
    c = getchar();
  }
  a[i] = 0;
  return i;
}
int main() {
  int n, k;
  scani(n), scani(k);
  if (n < k || (n > 1 && k == 1)) {
    puts("-1");
    return 0;
  }
  int limit = max(0, k - 2);
  for (int i = 0; i + limit < n; i++) printf("%c", (i & 1) + 'a');
  for (int i = 2; i < k; i++) printf("%c", i + 'a');
  return 0;
}

```