Walk Alone is playing roulette, a kind of gambling. For simplification, we assume its rules and steps as follows:

• The whole gambling process composes of many turns.

• In the -th turn:

• Walk Alone can choose an integer and pay yuan as the wager.

• If Walk Alone wins, he will get yuan from the maker, which means he gains yuan in this turn. Otherwise, the maker will devour the yuan he has paid, which means he loses yuan in this turn. The probability that Walk Alone wins is .

Walk Alone has yuan initially, and he wants to earn an extra yuan. He will use the following strategy to gamble:

• In the first turn, Walk Alone pays yuan as the wager, i.e., .

• If Walk Alone wins in the -th turn, then . Otherwise, .

• At the beginning of each turn, if Walk Alone has at least yuan, then he gets satisfied and quits the game. Otherwise, he must pay yuan as the wager, and he will have to stop gambling if he has less than yuan.

 Walk Alone's good friend, Kelin wants to exhort him not to gamble. Tell him the probability that he successfully earns an extra yuan.

输入描述:

The only line of the input contains two integers  and , indicating the initial amount of money and the amount of money Walk Alone wants to earn.

输出描述:

Output the probability that Walk Alone successfully earns an extra  yuan modulo . It can be shown that the answer can always be expressed as an irreducible fraction , where  and  are integers and . Output such an integer  that  and .

2 2

623902721

5 30

79070907

备注:

In the first example, Walk Alone has  yuan initially.
In the first turn, he pays  yuan as the wager, and he has  yuan left. He must win the turn, or in the next turn he will have to pay  yuan, and he does not have enough money. The probability that he wins is .
In the second turn, he pays  yuan and has  yuan left. If he wins the turn, he will have  yuan, which reaches his goal. Otherwise, he will have to pay  yuan in the third turn, and he must win the turn to reach his goal. Hence the total probability is .