import std.conv, std.functional, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }


enum MO = 10L^^9 + 7;

long power(long a, long e) {
  long x = a % MO, y = 1;
  for (; e; e >>= 1) {
    if (e & 1) {
      y = (y * x) % MO;
    }
    x = (x * x) % MO;
  }
  return y;
}

int N;
long[] P, K;

void main() {
  try {
    for (; ; ) {
      N = readInt();
      P = new long[N];
      K = new long[N];
      foreach (i; 0 .. N) {
        P[i] = readLong();
        K[i] = readLong();
      }
      
      long[long] qlss;
      foreach (i; 0 .. N) {
        long[long] qls;
        if (P[i] == 2) {
          // 3
          qls = [3: 1];
        } else if (P[i] == 5) {
          // 20
          qls = [2: 2, 5: 1];
        } else {
          bool check(long e) {
            long[2] mul(in long[2] a, in long[2] b) {
              return [(a[0] * b[0] + a[1] * b[1]) % P[i], (a[0] * b[1] + a[1] * b[0] + a[1] * b[1]) % P[i]];
            }
            long[2] x = [0, 1], y = [1, 0];
            for (; e; e >>= 1) {
              if (e & 1) {
                y = mul(y, x);
              }
              x = mul(x, x);
            }
            return (y == [1, 0]);
          }
          long period;
          long m = (P[i] % 5 == 1 || P[i] % 5 == 4) ? (P[i] - 1) : (2 * (P[i] + 1));
          for (long d = 1; d * d <= m; ++d) {
            if (m % d == 0) {
              if (check(d)) {
                period = d;
                break;
              }
              if (check(m / d)) {
                period = m / d;
              }
            }
          }
          assert(period > 0);
          for (long q = 2; q * q <= period; ++q) {
            if (period % q == 0) {
              long l;
              do {
                ++l;
                period /= q;
              } while (period % q == 0);
              qls[q] = l;
            }
          }
          if (period > 1) {
            qls[period] = 1;
          }
        }
        debug {
          writefln("period mod %s = %s", P[i], qls);
        }
        qls.update(P[i], () => (K[i] - 1), (ref long l) => (l + K[i] - 1));
        foreach (q, l; qls) {
          qlss.update(q, () => l, (ref long lMax) => max(lMax, l));
        }
      }
      debug {
        writeln(qlss);
      }
      long ans = 1;
      foreach (q, l; qlss) {
        ans *= power(q, l);
        ans %= MO;
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}