Statement

There are $N$ teams participating in the chess team competition. Each team consists of $M$ players. The competition adopts a round-robin system, and a total of $\frac{N(N-1)}{2}$ matches will be played. In each match, the $M$ players from both teams will be randomly paired for a game, and a winner will be determined in each game. After all matches are over, each player will have played exactly $N-1$ games. If a player wins all games, they will receive the undefeated award. Please find the maximum number of players who can possibly receive the undefeated award.

Input

The input consists of a single line containing two space-separated integers $N$ and $M$, indicating that there are $N$ teams and each team has $M$ players ($2 \leqslant N \leqslant 10^9$, $1 \leqslant M \leqslant 10^9$).

Output

Output a single number $t$ representing the maximum number of players who can potentially win the undefeated award.

Samples

3 3

4

1 1

1

Notes

For the $1$st test case, assume that there are $3$ teams participating in the competition.

1. Team $T$: players $T_1, T_2, T_3$;
2. Team $W$: players $W_1, W_2, W_3$;
3. Team $R$: players $R_1, R_2, R_3$;

The results of the competition may be as follows:

• Team $T$ vs. Team $W$ :
  • $T_1$ vs. $W_1$, $W_1$ wins
  • $T_2$ vs. $W_2$, $W_2$ wins
  • $T_3$ wins against $W_3$
• Team $T$ vs. Team $R$
  • $T_1$ wins against $R_3$
  • $T_2$ vs. $R_1$, $R_1$ wins
  • $T_3$ wins against $R_2$
• Team $W$ vs. Team $R$
  • $W_1$ vs. $R_3$, $R_3$ wins
  • $W_2$ vs. $R_2$, $R_2$ wins
  • $W_3$ wins against $R_1$

At this time, only player $T_3$ from team $T$ won the undefeated award. In this example, the maximum number of players who could potentially win the undefeated award is $4$.