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F. Koala and Notebook

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputKoala Land consists of $$$m$$$ bidirectional roads connecting $$$n$$$ cities. The roads are numbered from $$$1$$$ to $$$m$$$ by order in input. It is guaranteed, that one can reach any city from every other city.

Koala starts traveling from city $$$1$$$. Whenever he travels on a road, he writes its number down in his notebook. He doesn't put spaces between the numbers, so they all get concatenated into a single number.

Before embarking on his trip, Koala is curious about the resulting number for all possible destinations. For each possible destination, what is the smallest number he could have written for it?

Since these numbers may be quite large, print their remainders modulo $$$10^9+7$$$. Please note, that you need to compute the remainder of the minimum possible number, not the minimum possible remainder.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 10^5, n - 1 \le m \le 10^5$$$), the number of cities and the number of roads, respectively.

The $$$i$$$-th of the following $$$m$$$ lines contains integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i, y_i \le n$$$, $$$x_i \ne y_i$$$), representing a bidirectional road between cities $$$x_i$$$ and $$$y_i$$$.

It is guaranteed, that for any pair of cities there is at most one road connecting them, and that one can reach any city from every other city.

Output

Print $$$n - 1$$$ integers, the answer for every city except for the first city.

The $$$i$$$-th integer should be equal to the smallest number he could have written for destination $$$i+1$$$. Since this number may be large, output its remainder modulo $$$10^9+7$$$.

Examples

Input

11 10 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11

Output

1 12 123 1234 12345 123456 1234567 12345678 123456789 345678826

Input

12 19 1 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 3 11 11 12 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10

Output

1 12 13 14 15 16 17 18 19 1210 121011

Input

12 14 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 1 3 1 4 1 10

Output

1 12 13 134 1345 13456 1498 149 14 1410 141011

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