Codeforces Round 439 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

brute force

dfs and similar

graphs

*2800

No tag edit access

The problem statement has recently been changed. View the changes.

×
D. The Overdosing Ubiquity

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe fundamental prerequisite for justice is not to be correct, but to be strong. That's why justice is always the victor.

The Cinderswarm Bee. Koyomi knows it.

The bees, according to their nature, live in a tree. To be more specific, a complete binary tree with *n* nodes numbered from 1 to *n*. The node numbered 1 is the root, and the parent of the *i*-th (2 ≤ *i* ≤ *n*) node is . Note that, however, all edges in the tree are undirected.

Koyomi adds *m* extra undirected edges to the tree, creating more complication to trick the bees. And you're here to count the number of simple paths in the resulting graph, modulo 10^{9} + 7. A simple path is an alternating sequence of adjacent nodes and undirected edges, which begins and ends with nodes and does not contain any node more than once. Do note that a single node is also considered a valid simple path under this definition. Please refer to the examples and notes below for instances.

Input

The first line of input contains two space-separated integers *n* and *m* (1 ≤ *n* ≤ 10^{9}, 0 ≤ *m* ≤ 4) — the number of nodes in the tree and the number of extra edges respectively.

The following *m* lines each contains two space-separated integers *u* and *v* (1 ≤ *u*, *v* ≤ *n*, *u* ≠ *v*) — describing an undirected extra edge whose endpoints are *u* and *v*.

Note that there may be multiple edges between nodes in the resulting graph.

Output

Output one integer — the number of simple paths in the resulting graph, modulo 10^{9} + 7.

Examples

Input

3 0

Output

9

Input

3 1

2 3

Output

15

Input

2 4

1 2

2 1

1 2

2 1

Output

12

Note

In the first example, the paths are: (1); (2); (3); (1, 2); (2, 1); (1, 3); (3, 1); (2, 1, 3); (3, 1, 2). (For the sake of clarity, the edges between nodes are omitted since there are no multiple edges in this case.)

In the second example, the paths are: (1); (1, 2); (1, 2, 3); (1, 3); (1, 3, 2); and similarly for paths starting with 2 and 3. (5 × 3 = 15 paths in total.)

In the third example, the paths are: (1); (2); any undirected edge connecting the two nodes travelled in either direction. (2 + 5 × 2 = 12 paths in total.)

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/26/2024 19:08:57 (k3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|