Problem1633--New Year and Old Subsequence

1633: New Year and Old Subsequence

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A string t is called nice if a string "2017" occurs in t as a subsequence but a string "2016" doesn't occur in t as a subsequence. For example, strings "203434107" and "9220617" are nice, while strings "20016", "1234" and "20167" aren't nice.

The ugliness of a string is the minimum possible number of characters to remove, in order to obtain a nice string. If it's impossible to make a string nice by removing characters, its ugliness is -1.

Limak has a string s of length n, with characters indexed 1 through n. He asks you q queries. In the i-th query you should compute and print the ugliness of a substring (continuous subsequence) of s starting at the index ai and ending at the index bi (inclusive).

Input

The first line of the input contains two integers n and q (4≤n≤200000, 1≤q≤200000)− the length of the string s and the number of queries respectively.

The second line contains a string s of length n. Every character is one of digits '0'—'9'.

The i-th of next q lines contains two integers ai and bi (1≤ai≤bi≤n), describing a substring in the i-th query.

Output

For each query print the ugliness of the given substring.

Examples
Input
8 3
20166766
1 8
1 7
2 8
Output
4
3
-1
Input
15 5
012016662091670
3 4
1 14
4 15
1 13
10 15
Output
-1
2
1
-1
-1
Input
4 2
1234
2 4
1 2
Output
-1
-1
Note

In the first sample:

  • In the first query, ugliness("20166766")=4 because all four sixes must be removed.
  • In the second query, ugliness("2016676")=3 because all three sixes must be removed.
  • In the third query, ugliness("0166766")=-1 because it's impossible to remove some digits to get a nice string.

In the second sample:

  • In the second query, ugliness("01201666209167")=2. It's optimal to remove the first digit '2' and the last digit '6', what gives a string "010166620917", which is nice.
  • In the third query, ugliness("016662091670")=1. It's optimal to remove the last digit '6', what gives a nice string "01666209170".

Source/Category

 
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