Charges solution codechef

Charges solution codechef

There are NN subatomic particles lined up in a row. There are two types: protons and electrons. Protons have a positive charge and are represented by 11, while electrons have a negative charge and are represented by 00.

Our current understanding of physics gives us a way to predict how the particles will be spaced out, if we know their charges. Two adjacent particles will be separated by 11 unit if they have opposite charges, and 22 units if they have the same charge.

When Chef is not in the kitchen, he is doing physics experiments on subatomic particles. He is testing the hypothesis by having NN particles in a row, and he will change the charge of a particle KK times. In the ii-th update, he will change the charge of the QiQi-th particle. After each update, find the distance between the first and last particle.

Note: Each update is persistent for further updates.

Input Charges solution codechef

  • The first line contains an integer TT, the number of test cases. Then the test cases follow.
  • Each test case contains three lines of input.
  • The first line contains two integers NNKK.
  • The second line contains a string SS of length NN, where SiSi represents the initial charge on ii-th particle.
  • The third line contains KK integers Q1,Q2,,QKQ1,Q2,…,QK, the positions of the changed particles.

Output Charges solution codechef

For each test case, output KK lines, where the ii-th line contains the answer after the updates Q1,,QiQ1,…,Qi have been made.

Constraints Charges solution codechef

  • 1T51≤T≤5
  • 1N,K1051≤N,K≤105
  • SS contains only 00 and 11 characters.
  • 1QiN1≤Qi≤N
  • The sum of KK over all testcases is at most 21052⋅105

Subtasks Charges solution codechef

Subtask #1 (100 points): original constraints

Sample Input Charges solution codechef

3 3
2 1 3

Sample Output Charges solution codechef


Explanation Charges solution codechef

Update 1: After reversing the parity of particle 22, the new configuration is 000000. Since all the particles have a similar charge, each is separated from the previous by a distance of 22 units. So the location of particle 33 is 2+2=42+2=4 units from the first particle.

Update 2: After reversing the parity of particle 11, the new configuration is 100100. Here, the charges of particles 11 and 22 differ, so they are separated by 11 unit. The charges of particles 22 and 33 agree, so they are separated by 22 units. So, the location of particle 33 is 1+2=31+2=3 units from the first particle.

Update 3: After reversing the charge of particle 33, the new configuration is 101101. Here, particles 11 and 22 are separated by 11 unit and particles 22 and 33 are separated by 11 unit. So the location of particle 33 is 1+1=21+1=2 units from the first particle.


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