CF580E.Kefa and Watch

One day Kefa the parrot was walking down the street as he was on the way home from the restaurant when he saw something glittering by the road. As he came nearer he understood that it was a watch. He decided to take it to the pawnbroker to earn some money.

The pawnbroker said that each watch contains a serial number represented by a string of digits from 0 to 9, and the more quality checks this number passes, the higher is the value of the watch. The check is defined by three positive integers l, r and d. The watches pass a check if a substring of the serial number from l to r has period d. Sometimes the pawnbroker gets distracted and Kefa changes in some substring of the serial number all digits to c in order to increase profit from the watch.

The seller has a lot of things to do to begin with and with Kefa messing about, he gave you a task: to write a program that determines the value of the watch.

Let us remind you that number x is called a period of string s (1 ≤ x ≤ |s|), if s__i  =  s__i + x for all i from 1 to |s|  -  x.

一天，鹦鹉基法在从餐厅回家的路上沿街行走，忽然看见路边有什么东西在闪闪发光。他走近一看，发现是一块手表。他决定把手表拿去当铺，换点钱。

当铺老板说，每块手表都有一个由数字 0 到 9 组成的字符串形式的序列号，该序列号通过的质量检测越多，手表的价值就越高。每次检测由三个正整数 $l$、$r$ 和 $d$ 定义：若序列号中从位置 $l$ 到 $r$ 的子串具有周期 $d$，则该手表通过此次检测。有时当铺老板会分心，此时基法便会将序列号的某个子串中的所有数字全部改为数字 $c$，以提高手表的收益。

老板一开始事情就很多，再加上基法捣乱，于是把这项任务交给了你：编写一个程序来确定手表的价值。

我们提醒你，称一个数 $x$（满足 $1 \le x \le |s|$）为字符串 $s$ 的周期，当且仅当对所有 $i$（$1 \le i \le |s| - x$），均有 $s_i = s_{i+x}$。

The first line of the input contains three positive integers n, m and k (1 ≤ n ≤ 105, 1 ≤ m + k ≤ 105) — the length of the serial number, the number of change made by Kefa and the number of quality checks.

The second line contains a serial number consisting of n digits.

Then m + k lines follow, containing either checks or changes.

The changes are given as 1 l r c (1 ≤ l ≤ r ≤ n, 0 ≤ c ≤ 9). That means that Kefa changed all the digits from the l-th to the r-th to be c.

The checks are given as 2 l r d (1 ≤ l ≤ r ≤ n, 1 ≤ d ≤ r - l + 1).

输入的第一行包含三个正整数 $n$、$m$ 和 $k$（$1 ≤ n ≤ 10^5$，$1 ≤ m + k ≤ 10^5$）——分别表示序列号的长度、Kefa 进行的修改次数以及质量检测次数。

第二行包含一个由 $n$ 个数字组成的序列号。

随后是 $m + k$ 行，每行描述一次检测或修改操作。

修改操作格式为 1 l r c（$1 ≤ l ≤ r ≤ n$，$0 ≤ c ≤ 9$），表示 Kefa 将第 $l$ 位至第 $r$ 位的所有数字均改为 $c$。

检测操作格式为 2 l r d（$1 ≤ l ≤ r ≤ n$，$1 ≤ d ≤ r - l + 1$）。

For each check on a single line print "YES" if the watch passed it, otherwise print "NO".

对于每一行的检查，如果手表通过了该检查，则输出 “YES”，否则输出 “NO”。

In the first sample test two checks will be made. In the first one substring "12" is checked on whether or not it has period 1, so the answer is "NO". In the second one substring "88", is checked on whether or not it has period 1, and it has this period, so the answer is "YES".

In the second statement test three checks will be made. The first check processes substring "3493", which doesn't have period 2. Before the second check the string looks as "334334", so the answer to it is "YES". And finally, the third check processes substring "8334", which does not have period 1.

在第一个样例测试中，将进行两次检查。第一次检查子串“12”是否具有周期 1，答案为“NO”。第二次检查子串“88”是否具有周期 1，该子串确实具有此周期，因此答案为“YES”。

在第二个样例测试中，将进行三次检查。第一次检查处理子串“3493”，它不具有周期 2。第二次检查前，字符串变为“334334”，因此该次检查的答案为“YES”。最后，第三次检查处理子串“8334”，它不具有周期 1。