Problem Description
As is known to all, MZL is an extraordinarily lovely girl. One day, MZL was playing with her favorite data structure, strings.
MZL is really like
Fibonacci Sequence, so she defines
Fibonacci Strings in the similar way. The definition of
Fibonacci Strings is given below.
1)
fib1=b
2)
fib2=a
3)
fibi=fibi−1fibi−2, i>2
For instance,
fib3=ab, fib4=aba, fib5=abaab.
Assume that a string
s whose length is
n is
s1s2s3...sn. Then
sisi+1si+2si+3...sj is called as a substring of
s, which is written as
s[i:j].
Assume that
i<n. If
s[1:i]=s[n−i+1:n], then
s[1:i] is called as a
Border of
s. In
Borders of
s, the longest
Border is called as
s'
LBorder. Moreover,
s[1:i]'s
LBorder is called as
LBorderi.
Now you are given 2 numbers
n and
m. MZL wonders what
LBorderm of
fibn is. For the number can be very big, you should just output the number modulo
258280327(=2×317+1).
Note that
1≤T≤100, 1≤n≤103, 1≤m≤|fibn|.
Input
T, which means the number of test cases.
Then for the following
T lines, each has two positive integers
n and
m, whose meanings are described in the description.
Output
T lines. Each has one number, meaning fibn's LBorderm modulo 258280327(=2×317+1).
Sample Input
2
4 3
5 5
Sample Output
1 2
找找规律，然后模拟一下,注意有大数
import java.io.*;
import java.math.BigInteger;
import java.util.*;
public class Main
{
public static void main(String args[])
{
Scanner cin = new Scanner(System.in);
BigInteger f[][] = new BigInteger[1005][3];
int i;
f[0][1]=BigInteger.ZERO;
f[0][2]=BigInteger.ZERO;
f[1][1]=BigInteger.ZERO;
f[1][2]=BigInteger.ZERO;
f[0][0]=BigInteger.ONE;
f[1][0]=BigInteger.ONE;
for (i=2;i<=1000;i++)
{
f[i][0]=f[i-1][0].add(f[i-2][0]);
f[i][1]=f[i-1][2].subtract(f[i-1][1]);
f[i][2]=f[i][1].add(f[i][0]).subtract(BigInteger.ONE);
}
int T=cin.nextInt();
for(;T>=1;T--)
{
int n;
BigInteger m;
n=cin.nextInt();
m=cin.nextBigInteger();
for(i=1;i<=1000;i++)
{
if(m.compareTo(f[i][0])<1)
{
m=f[i][1].add(m).subtract(BigInteger.ONE);
m=m.mod(BigInteger.valueOf(258280327));
System.out.println(m);
break;
}
else
m=m.subtract(f[i][0]);
}
}
}
}
