module main; // https://kmjp.hatenablog.jp/entry/2015/02/09/0900 より // フィボナッチ数列、行列累乗 import std; struct ModInt(long MOD) { private: long val; public: // コンストラクタ // useMod:MODで剰余を取る処理を行うかどうか this(long x, bool useMod = true) { if (useMod) { val = x % MOD; if (val < 0) val += MOD; } else val = x; } @property long value() const { return val; } @property ModInt value(long x) { val = x % MOD; if (val < 0) val += MOD; return this; } // 代入演算子 ModInt opAssign(T)(T x) if (isIntegral!T) { val = x % MOD; if (val < 0) val += MOD; return this; } // 演算代入演算子 ModInt opOpAssign(string op, T)(T rhs) pure nothrow if (is(T : ModInt) && (op == "+" || op == "-" || op == "*" || op == "/")) { static if (op == "+") { val += rhs.val; while (val >= MOD) val -= MOD; } else static if (op == "-") { val -= rhs.val; while (val < 0) val += MOD; } else static if (op == "*") { val = val * rhs.val % MOD; while (val < 0) val += MOD; } else static if (op == "/") { val = val * rhs.inv().val % MOD; while (val < 0) val += MOD; } return this; } ModInt opOpAssign(string op, T)(T rhs) pure nothrow if (isIntegral!T && (op == "+" || op == "-" || op == "*" || op == "/")) { static if (op == "+") { val += rhs; while (val >= MOD) val -= MOD; } else static if (op == "-") { val -= rhs; while (val < 0) val += MOD; } else static if (op == "*") { val = val * rhs % MOD; while (val < 0) val += MOD; } else static if (op == "/") { val = val * Mint(rhs).inv().val % MOD; while (val < 0) val += MOD; } return this; } // 二項演算子 ModInt opBinary(string op, T)(T rhs) pure nothrow if (is(T : ModInt) && (op == "+" || op == "-" || op == "*" || op == "/")) { auto r = this; return r.opOpAssign!op(rhs); } ModInt opBinary(string op, T)(T rhs) pure nothrow if (isIntegral!T && (op == "+" || op == "-" || op == "*" || op == "/")) { auto r = this; return r.opOpAssign!op(rhs); } ModInt opBinaryRight(string op, T)(T lhs) pure nothrow if (isIntegral!T && (op == "+" || op == "-" || op == "*" || op == "/")) { ModInt r = lhs; return r.opOpAssign!op(this); } // 単項演算子 ModInt opUnary(string op)() pure nothrow if (op == "++" || op == "--") { static if (op == "++") { ++val; if (val == MOD) val = 0; } else static if (op == "--") { if (val == 0) val = MOD; --val; } return this; } ModInt opUnary(string op)() pure const nothrow if (op == "-") { if (val == 0) return ModInt(0, false); else return ModInt(MOD - val, false); } // 等号演算子 bool opEquals(ref const ModInt rhs) @safe pure const nothrow { return val == rhs.val; } bool opEquals(T)(const T rhs) @safe pure const nothrow if (isIntegral!T) { return val == rhs; } // 累乗 ModInt pow(T)(T n) pure const if (isIntegral!T) { ModInt x = n >= 0 ? this : inv(), r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } // MODに関する逆元 ModInt inv() pure const { long a = val, b = MOD, u = 1, v = 0; while (b) { long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } return ModInt(u); } string toString() pure nothrow const { return val.to!string; } // 連想配列のためのハッシュ hash_t toHash() const @safe pure nothrow { // MMIX by Donald Knuth return cast(hash_t)(6_364_136_223_846_793_005L * val + 1_442_695_040_888_963_407L); } } immutable MOD = 10L ^^ 9 + 7; alias Mint = ModInt!MOD; alias Mat = Mint[2][2]; Mat mul(Mat A, Mat B) { Mat C; C[0][0] = A[0][0] * B[0][0] + A[0][1] * B[1][0]; C[0][1] = A[0][0] * B[0][1] + A[0][1] * B[1][1]; C[1][0] = A[1][0] * B[0][0] + A[1][1] * B[1][0]; C[1][1] = A[1][0] * B[0][1] + A[1][1] * B[1][1]; return C; } Mat pow(Mat A, long p) { Mat R = [[Mint(1), Mint(0)], [Mint(0), Mint(1)]]; while (p) { if (p & 1) R = mul(A, R); A = mul(A, A); p >>= 1; } return R; } Mint pat(long c) { Mat A = [[Mint(1), Mint(1)], [Mint(1), Mint(0)]]; Mat B = pow(A, c - 1); return B[0][0] + B[0][1] + B[1][0] + B[1][1]; } void main() { // 入力 int N = readln.chomp.to!int; // 答えの計算 Mint ans = 1; foreach (_; 0 .. N) { long C; string S; readln.chomp.formattedRead("%d %s", C, S); auto D = BigInt(S); if (D > MOD - 1) D %= MOD - 1; ans *= pat(C).pow(cast(long)D); } // 答えの出力 writeln(ans); }