Jee, You See? solution codeforces

During their training for the ICPC competitions, team “Jee You See” stumbled upon a very basic counting problem. After many “Wrong answer” verdicts, they finally decided to give up and destroy turn-off the PC. Now they want your help in up-solving the problem.

You are given 4 integers $n$ , $l$ , $r$ , and $z$ . Count the number of arrays $a$ of length $n$ containing non-negative integers such that:

$l \leq a_{1} + a_{2} + \dots + a_{n} \leq r$ , and
$a_{1} \oplus a_{2} \oplus \dots \oplus a_{n} = z$ , where $\oplus$ denotes the bitwise XOR operation.

Since the answer can be large, print it modulo $10^{9} + 7$ .

Input

Jee, You See? solution codeforces

The only line contains four integers $n$ , $l$ , $r$ , $z$ ( $1 \leq n \leq 1000$ , $1 \leq l \leq r \leq 10^{18}$ , $1 \leq z \leq 10^{18}$ ).

Output

Print the number of arrays $a$ satisfying all requirements modulo $10^{9} + 7$ .

Examples

input

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3 1 5 1

output

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input

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4 1 3 2

output

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input

Jee, You See? solution codeforces

Copy

2 1 100000 15629

output

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input

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100 56 89 66

output

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981727503

Note

The following arrays satisfy the conditions for the first sample:

$[1, 0, 0]$ ;
$[0, 1, 0]$ ;
$[3, 2, 0]$ ;
$[2, 3, 0]$ ;
$[0, 0, 1]$ ;
$[1, 1, 1]$ ;
$[2, 2, 1]$ ;
$[3, 0, 2]$ ;
$[2, 1, 2]$ ;
$[1, 2, 2]$ ;
$[0, 3, 2]$ ;
$[2, 0, 3]$ ;
$[0, 2, 3]$ .

The following arrays satisfy the conditions for the second sample:

$[2, 0, 0, 0]$ ;
$[0, 2, 0, 0]$ ;
$[0, 0, 2, 0]$ ;
$[0, 0, 0, 2]$ .

Jee, You See? solution codeforces

Jee, You See? solution codeforces

Jee, You See? solution codeforces

Solution

“Click here“

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