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Statement

$N$ teams participate in a chess team tournament. Each team consists of $M$ players. The tournament uses a round-robin format, with a total of $\frac{N(N-1)}{2}$ games. In each game, the $M$ players from the two teams are randomly paired to play against each other, and each game is guaranteed to have a winner. After all games are completed, each player has played exactly $N-1$ games. If a player wins all games, they receive a win-win bonus. Find the maximum number of players who can receive a win-win bonus.

Input

The input consists of a single line of two numbers, $N,M$, separated by a space, representing $N$ teams and $M$ players per team ($2 \leq N \leq 10^9$, $1 \leq M \leq 10^9$).

Output

The output is a single number, $t$, representing the maximum number of players who can win the perfect victory prize.

Samples

3 3

4

1 1

1

Notes

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

• Team $T$: Players $T_1, T_2, T_3$;

• Team $W$: Players $W_1, W_2, W_3$;

• Team $R$: Players $R_1, R_2, R_3$;

The possible results of the game are as follows:

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

At this point, only player $T_3$ from team $T$ wins the perfect victory prize. In this example, the maximum number of players who could win the perfect victory prize is $4$.