Codeforces 239C Not Wool Sequences【规律】

最新推荐文章于 2021-09-27 21:08:34 发布

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A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r(1 ≤ l ≤ r ≤ n) such that $\text{[math]}$ . In other words each wool sequence contains a subsequence of consecutive elements with xor equal to 0.

The expression $\text{[math]}$ means applying the operation of a bitwise xor to numbers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is marked as "^", in Pascal — as "xor".

In this problem you are asked to compute the number of sequences made of n integers from 0 to 2m - 1 that are not a wool sequence. You should print this number modulo 1000000009 (109 + 9).

Input

The only line of input contains two space-separated integers n and m (1 ≤ n, m ≤ 105).

Output

Print the required number of sequences modulo 1000000009 (109 + 9) on the only line of output.

Examples

input
3 2

output
6

Note

Sequences of length 3 made of integers 0, 1, 2 and 3 that are not a wool sequence are (1, 3, 1), (1, 2, 1), (2, 1, 2), (2, 3, 2), (3, 1, 3) and (3, 2, 3).

题目大意：

构造一个长度为N的一个序列，其中元素只能是0~2^m-1；

构造出来的序列需要保证任意区间内的亦或值不能为0.；

思路：

暴力打表找找规律就行了。

不难发现其如果n==1的时候，结果就是2^m-1；

如果n>1的时候，是随着n的递增，而成倍数递增的。

具体规律参考一下代码就行了。

Ac代码：

#include<stdio.h>
#include<string.h>
using namespace std;
__int64 mod=1000000009;
__int64 mi(__int64 a,__int64 b)
{
    __int64 ans=1;
    a%=mod;
    while(b>0)
    {
        if(b%2==1)ans=(ans*a)%mod;
        b/=2;
        a=(a*a)%mod;
    }
    return ans;
}
int main()
{
    int n,m;
    while(~scanf("%d%d",&n,&m))
    {
        __int64 ans=mi(2,m);
        ans-=1;
        __int64 temp=ans-1;
        ans=(ans%mod+mod)%mod;
        temp=(temp%mod+mod)%mod;
        for(int i=2;i<=n;i++)
        {
            ans*=temp;
            ans%=mod;
            temp--;
            temp=(temp%mod+mod)%mod;
        }
        printf("%I64d\n",ans%mod);
    }
}