Problem:
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問題文

有理数列 $X_0, X_1, X_2, ..., X_N$ がある。各項は以下のように定義される。

$X_0 = 0$

$X_i = X_{i-1}$ $op_i$ $Y_i$ ($1 \leq i \leq N$). ただし $op_i$ は $＋$、$−$、$×$、$÷$のいずれかである。

$X_N$ を求めよ。

入力

入力は以下の形式に従う。与えられる数は全て整数である。

$N$
$o_1$ $Y_1$
$o_2$ $Y_2$
$...$
$o_N$ $Y_N$

$o_i = 1$ のとき $op_i$ は＋、$o_i = 2$ のとき $op_i$ は−、$o_i = 3$ のとき $op_i$ は×、$o_i = 4$ のとき $op_i$ は÷である。

制約

$1 \leq N \leq 10^5$

$1 \leq o_i \leq 4$

$-10^6 \leq Y_i \leq 10^6$

$o_i=4$ ならば $Y_i \neq 0$

$X_N$ は $-2^{31}$ 以上 $2^{31}$ 未満の整数となる。

出力

$X_N$ の値を1行に出力せよ。

Sample Input 1

4
1 1
4 2
2 4
3 4

Output for the Sample Input 1

-14

$X_0 = 0$

$X_1 = X_0 ＋ 1 = 1$

$X_2 = X_1 ÷ 2 = 1/2$

$X_3 = X_2 − 4 = -7/2$

$X_4 = X_3 × 4 = -14$

Solution in JAVA (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	public static void main(String[] args) {
		IO io = new IO();
		int n = io.nextInt();
		BigInteger x = BigInteger.ZERO;
		BigInteger MOD = BigInteger.valueOf((1L<<62)+1).nextProbablePrime();
		for(int i=0;i<n;i++) {
			int o = io.nextInt();
			BigInteger y = new BigInteger(io.next());
			switch (o) {
			case 1:
				x = x.add(y).remainder(MOD);
				break;
			case 2:
				x = x.subtract(y).add(MOD).remainder(MOD);
				break;
			case 3:
				x = x.multiply(y).remainder(MOD);
				break;
			case 4:
				x = x.multiply(y.modInverse(MOD)).remainder(MOD);
				break;
			}
		}
		//System.out.println(x);
		if (x.compareTo(BigInteger.valueOf(1L<<31)) > 0) {
			x = x.subtract(MOD);
		}
		System.out.println(x);
	}

}
class IO {
	private final InputStream in;
	private final PrintWriter out = new PrintWriter(System.out);
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public IO() { this(System.in);}
	public IO(InputStream source) { this.in = source;}
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	private static boolean isNewLine(int c) { return c == '\n' || c == '\r';}
	private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
	private void skipNewLine() { while(hasNextByte() && isNewLine(buffer[ptr])) ptr++;}
	public boolean hasNext() { skipUnprintable(); return hasNextByte();}
	public boolean hasNextLine() { skipNewLine(); return hasNextByte();}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public char[] nextCharArray(int len) {
		char[] s = new char[len];
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		int i = 0;
		int b = readByte();
		while(isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}
	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}
	public double nextDouble() { return Double.parseDouble(next());}
	public int[] arrayInt(int n) { int[] a = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a;}
	public long[] arrayLong(int n) { long[] a = new long[n]; for(int i=0;i<n;i++) a[i] = nextLong(); return a;}
	public double[] arrayDouble(int n) { double[] a = new double[n]; for(int i=0;i<n;i++) a[i] = nextDouble(); return a;}
	public void arrayInt(int[]... a) {for(int i=0;i<a[0].length;i++) for(int j=0;j<a.length;j++) a[j][i] = nextInt();}
	public int[][] matrixInt(int n,int m) { int[][] a = new int[n][m]; for(int i=0;i<n;i++) a[i] = arrayInt(m); return a;}
	public char[][] charMap(int n,int m) { char[][] a = new char[n][m]; for(int i=0;i<n;i++) a[i] = nextCharArray(m); return a;}
	public void println(long x) { out.println(x);}
	public void println(double x) { out.println(x);}
	public void println(String s) { out.println(s);}
	public void println() { out.println(); }
	public void print(long x) { out.print(x); }
	public void print(double x) { out.print(x); }
	public void print(String s) { out.print(s); }
	public void print(char c) {out.print(c);}
	public void flush() {out.flush(); }
}