MZL's Border
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 657 Accepted Submission(s): 203
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|
.
MZL is really like
1)
2)
3)
For instance,
Assume that a string
Assume that
Now you are given 2 numbers
Note that
Input
The first line of the input is a number
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.
Then for the following
Output
The output consists of
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
import java.io.*;
import java.math.*;
import java.util.*;
public class Main {
/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
BigInteger[] f = new BigInteger[3004];
f[0]=BigInteger.ONE;
f[1]=BigInteger.ONE;
int i;
for(i=2;i<3003;i++){
f[i]=f[i-1].add(f[i-2]);
}
Scanner cin = new Scanner(System.in);
int T = cin.nextInt();
for(;T>=1;T--){
int n;
BigInteger m;
n=cin.nextInt();
m=cin.nextBigInteger();
BigInteger ans;
BigInteger mod = BigInteger.valueOf(258280327);
for(i=0;i<=n;i++){
if(m.compareTo(f[i].subtract(BigInteger.ONE))==-1) break;
}
ans=m.subtract(f[i-2]);
ans=ans.mod(mod);
System.out.println(ans);
}
}
}